Winter will be early in my country this year. I have Labrador that is going to be one year old by then. And during extreme cold, temperature may fall below 10 degrees Celsius, but no snowing. I have marble flooring which gets really cold during winter. So, do I have to buy boots for my pooch?
Have you ever seen wolves hunt in the snow wearing their winter boots? 😉
So the short answer is: No, unless there's a specific medical condition you don't.
Make sure the dog has a warm place to stay in rather than stand/sit on the cold floor all the time and you should be fine.
Far more important, depending on where you live, is cleaning the paws from salt (water) from roads as that can cause irritation or other issues (e.g. when licked on). Ideally this should happen after every walk, just using some warm water should be enough.
You can also buy special wax or sprays to better seal/protect the paws, but that's really optional, especially if your dog is not working (e.g. sled pulling).
Speaking of 10 'C (50 'F), last 3 weeks it's been around 52 'F (11 'C) in my house. I didn't turn on the heat yet, not until it drops below 48 'F (8 'C), as I am perfectly comfortable sleeping under my blanket at 9 'C.
I realize a Chukchi-bred Siberian husky's double coat is a bit tougher than Labrador's, but not that much, I'd guess.
That's 24/7, 7 days a week. About 7-8 months of the year. Remaining 4 months of the year, once it gets above 64 'F (18 'C), I run A/C to cool it down.
A +10C air temperature can only be considered"extreme" if you live in sub-Saharan climate. But perhaps you are just trolling?
Afaik, lab has a nice thick coat and the webbing on his paws. From experience with my Husky I know that the webbing grows linearly with the temperature. When it dropped to -50F last winter, her paw fur was about 4 inch long and as thick as her tail. A sight to behold, indeed.
Anecdotally, in Montana, when it was around -30F air (-40F wind-chill, -40 F = -40C) I spent an hour in a doggie park with my Husky. Out of around 20 doggies, not a single one had any boots. There were at least 4-6 labs, happily hopping about, without any boots whatsoever. Perhaps nobody told them it was cold. But it was only -30F, not +10C, so there's that...