Cats, dogs and people
Firstly I'd like to clarify the general facts between dogs and cats (and humans) and snake bites, before addressing the specific common european viper/adder (vipera berus) and where your assumptions are correct and incorrect.
The physiology between species varies, just as anatomy does. It this difference in physiology accounts for varying inter-species reactions.
The different species react differently to different types of venom.
For example from the University of Adelaide:
../.. Though they can cause neurotoxic paralysis (muscle weakness,
respiratory failure), this is uncommon to rare in humans, but common
in domestic animals (cats, dogs). ../..
Different venoms have different effects on the victim. For example, some venoms act as anti-coagulants, some as neuro-toxins, some cause musle or kidney damage. As there's subtle physiological differences between the species, this accounts for the difference in reactions. Just as some medicine is safe for human use and not pets.
The funnel web spider is highly venomous and potentially lethal to human beings, but not dogs or cats.
What is the world's most dangerous spider?
The Australian funnel-web spiders are among the deadliest spiders in
the world in the effect their bites have on humans and our primate
relations (although the bite has little effect on dogs and cats).
The physiology of this is described well here:
Why is funnel web spider venom so lethal to humans and not so much for other mammals?
Snakes can be lethal to both dogs and cats
Many snake bites can be venomous and lethal to cats. In Australia, for instance, there's many deadly snakes, that are lethal, not only to dogs and cats, but to humans.
From the RSPCA website:
The sort of reaction your pet has to a snake bite is determined by a
number of factors: the type of snake, the amount of venom injected and
the site of the snake bite. Generally the closer the bite is to the
heart the quicker the venom spreads to the rest of the body. In
addition, at the beginning of summer, snakes' venom glands are fuller
and their bites are much more severe.
The assumption that cats are not being injected with venom (having dry bites) is not altogether true.
From the RSPCA website:
Dogs will often try to chase or kill snakes resulting in snake bites
usually to the dog's face and legs. Cats, being hunters and chasing
anything that moves, are also quite susceptible to snake bites.
Cats actually receive more snake anti venom than both humans or dogs in some areas.
From ABC News
Each spring humans are warned of the dangers of snakes coming out of
hibernation, yet it is dogs and cats that receive more than 70 per
cent of administered antivenom. .
../..
"It’s the cats that we tend to see [which] have more of those
interactions than the dogs,"
../..
../.. cats may be at a higher risk of being bitten, ../..
The truth is, it's hard to obtain accurate statistics in some places about snake bite in our pets.
From Snake Bites and Dogs.
You won’t find details on the numbers of dogs bitten, or killed, by
venomous snakes, though. I asked Michael Schaer, DVM, Professor of
Veterinary Internal Medicine at the University of Florida, College of
Veterinary Medicine, about the numbers of dogs bitten or killed by
snakes in the U.S.
"I don't believe we have a valid source of information on the actual
numbers of dogs bitten or killed by snakes annually in the United
States," he explained, "because there is no central data resource for
this."
Cats survive snake bites more than dogs
It seems that cats are hardier when it comes to snake bites. They take longer to react and have a better survival rate both with and without anti-venom.
From ABC News
While cats may be at a higher risk of being bitten, dogs are more
susceptible to snake bites than cats, particularly to brown snakes,
which are more prevalent in the southern areas of South Australia.
"A bite for a dog can be lethal in less than 30 minutes."
Cats have a greater resistance to snake bites, but will succumb to
bites within 12 to 24 hours.
From Midland Vet Hospital
Cats tend to have milder signs than dogs. They will
often present as being ‘dizzy’ with dilated pupils and no ability to
blink. Dogs
can have a rapid onset of signs and many owners often do not notice
any signs before they collapse.
Survival Rates:
90-95% of cats will survive a snake bite
if treated with anti-venom. If not, the chance is
40-50%.70% of
dogs will survive with anti-venom, however only 5% of
dogs will survive if not treated with antivenom
However cats are more likely than dogs to have allergic reactions to snake bites.
From ABC News
was more common for cats to have an allergic reaction to a bite.
Types of venomous snakes
From the Taxonomy of venomous snakes:
Around a quarter of all snake species are identified as being
venomous.
In North America
Venomous snakes that your pet may be exposed to fall into two major
categories: the crotalids and the elapids. Crotalids belong to the pit
viper family and include snakes such as the copperheads, rattlesnakes,
and water moccasins (also known as cottonmouths). .../... The elapids
are the most deadly venomous snakes. Luckily, in North America the
coral snake is the only member of this group.
It should also be noted that the cost of treating a pet with anti-venom is expensive and this may or may not affect veterinarian advice, as the treatment can extend to $2-3000.
The common european viper/adder (vipera berus)
The vipera berus, although it is a venomous snake, it is not a particularly dangerous snake. It doesn't account for many deaths.
What usually happens to a cat when bitten is this the area bitten
swells a lot the cat has some pain and lays down to rest for 30
minutes to two hours depending on the amount of poison injected, and
then the swelling goes down and the cat is back to normal.
This is what happens in most cases of dog, cat and human bites by this snake.
Treatment of bites by adders and exotic venomous snakes doi: 10.1136/bmj.331.7527.1244
UK poisons centres are consulted about an average of 100 human and a
dozen veterinary cases each year. In about 70% of patients, envenoming
is negligible or purely local, causing pain, swelling, and
inflammation of the bitten digit.
../.. Only 14 fatalities have been reported since 1876 ../..
From the wikipedia link provided in the question:
Relatively speaking, bites from this species are not highly dangerous.
The potential for anaphylactic reaction and possible effects of the venom, is taken seriously, as although the risk is low, it's still dangerous and can cause the patient to become ill.
From the University of Adelaide:
Bites may cause mild to severe local effects, shock & coagulopathy.
All cases should be managed as potentially severe. Shock should be
monitored for and vigorously treated. Specific antivenom is available
only for some Vipera species, but should be used in all but minor
envenoming cases.
.../... All cases should be treated as urgent & potentially lethal.
Rapid assessment & commencement of treatment including appropriate
antivenom (if indicated & available) is mandatory. Admit all cases.
The common european viper/adder (vipera berus) and dogs
You describe the following symptoms if your cat is bitten by this snake.
when a dog gets bitten by this snake the dog must get to a vet within
30 minutes for treatment because it might be deadly for dogs.
As the poisons may be lethal to humans, it can also be lethal to dogs and cats. An anaphylactic (systemic) reaction can appear from 5 minutes or take many hours to show.
Treatment of bites by adders and exotic venomous snakes doi: 10.1136/bmj.331.7527.1244
Dramatic anaphylactoid symptoms may appear within five minutes of the
bite ../.. or may be delayed for many hours.
This study indicates that the venom can make dogs sick, but is not necessarily lethal as suggested in your question; The effect of a single dose of prednisolone in dogs envenomated by Vipera berus – a randomized, double-blind, placebo-controlled clinical trial doi: 10.1186/s12917-015-0352-6:
.../... A total of 75 dogs bitten by Vipera berus within the previous
24 hours were included. .../... None of the dogs died during the
study period.
It appears these dogs were not administered anti-venom.
This is the same reaction for both dogs and humans, but the symptoms last for longer. Unless of course there is an anaphylactic response in any of these species.
Treatment of bites by adders and exotic venomous snakes doi: 10.1136/bmj.331.7527.1244
Immediate sharp pain is followed, usually within a few minutes but
sometimes up to more than 30 minutes later, by a sensation of tingling
and local swelling that spreads proximally. Local blisters containing
blood are uncommon. Spreading pain, tenderness, inflammation (often
described misleadingly as “cellulitis,” although there is no
infection), and tender enlargement of regional lymph nodes are
sometimes noticeable within hours. Reddish lymphangitic lines and
bruising appear, and the whole limb may become swollen and bruised
within 24 hours (fig 2) with involvement of the trunk and, in
children, the whole body ../..
I cannot find any definitive difference between the reactions of dogs and cats and this particular snake bite, beyond the generalisation that cats tend to survive snake bites more so than dogs.
As for this statement:
A large dog can handle less snake venom then a tiny cat why is this?.
There is no where I can find evidence of this assertion. Toxicity usually correlates with the amount of toxin, time of year, site of the bite and size of the animal across the species.
From Merck Vet Manual:
Fatal snakebites are more common in dogs than in other domestic
animals. Because of the relatively small size of some dogs in
proportion to the amount of venom injected, the bite of even a small
snake may be fatal. In dogs and cats, mortality is generally higher in
bites to the thorax or abdomen than bites to the head or extremities. .../...
note they are comparing dog sizes to livestock.
The venom affects several physiological pathways Biological and biochemical activities of Vipera berus (European viper) venom.:
Vipera berus venom displayed in vitro proteolytic, fibrinolytic,
anticoagulant, and phospholipase A2 activities.
As for the exact physiological mechanism that differ between dogs and cats, I have not been able to isolate that (currently not having access to journals makes this difficult) and such a detailed review may be a better fit on Biology.Se.