Why is my dog limping in the winter time?

Your question likely needs to be answered by a vet. Maybe you can ask your parents why they are against it.

A vet visit, not including tests (usually all the lab work is most of the itemized expense), and medicine (the second most costly component) is fairly reasonable - approx. $50. Also some vets and groomers offer an à la carte service to trim the nails, including dew claws, for approx. $10-15. If they nip the quick and it starts bleeding, they use something to stop it, so the dog is not suffering in pain. In my opinion that’s well worth it. Also, in case expense is a reason: Many medications used for pets are also used for humans. So If vet recommends something like an antibiotic or pain reliever, you can ask if they will give a script for the correct dosage to be filled at your local pharmacy, which is usually a much lower cost.