I was wondering if it would be safe to chill in the fridge--or even freeze in the freezer before giving it to the dog. My guess is that it would either make it brittle and unsafe, or it would become a nice chilly treat for puppy teeth.
If you have decided that feeding rawhide to your dog is appropriate, I don't see why freezing them would be any cause for concern. Many dogs enjoy frozen treats.
There are a couple of lines of thought on if rawhide should be feed to a dog at all, these are addressed in our existing question Are rawhide bones or natural raw bones potentially dangerous for a dog?
I looked around for reference for or against, offering frozen rawhide treats to dogs. I did not find anything different then offering them unfrozen. Frozen hide/leather does not get brittle.
Yes, it is safe.
However, if I were you, I would consult the vet before making any big changes to your pets' food. Plus, rawhide isn't a great food source anyway. It's not exactly bad... but it's not great either. Just make sure that your vet is aware of this change. You know, just in case something happens.
Speaking from personal experience, freezing rawhide is safe, but I emphasize you should not do it unless your vet knows. Take that advice, it could be very helpful in the event of an emergency. Considering rawhide (warm or cool) has its risks. There's a lot of things that need to be considered. This article addresses safety of rawhide.
"Chewing also keeps dogs’ jaws strong, teeth clean, and breath a bit fresher. Dogs that chew regularly on rawhides and other bones or toys have less plaque and tartar build-up on teeth." So not only is it safe, but it's also got one or two benefits.
"Still, risks can be serious, so don’t ignore them. Weigh the risks and benefits of giving rawhides based upon your dog's chewing needs and behaviors. Contamination. As with pet toys, rawhide chews can contain trace amounts of toxic chemicals. And, as with other pet (or human) foods, Salmonella or E. coli contamination is possible. Even humans can be at risk when coming into contact with these bacteria on rawhide treats. Digestive irritation. Some dogs are simply sensitive or allergic to rawhide or other substances used in their manufacture. This can cause problems, including diarrhea. Choking or blockages. Rawhide bones and other edible chews can pose a choking and blockage risk. In fact, this is a much bigger risk than contamination or digestive irritation. If your dog swallows large pieces of rawhide, the rawhide can get stuck in the esophagus or other parts of the digestive tract. Depending on its size and where it is located, a vet may be able to remove these pieces fairly easily through the throat. But sometimes, abdominal surgery is needed to remove them from the stomach or intestines. If it isn’t resolved, a blockage can lead to death." So there's a lot of risks, but the chances are low.