Growing up in the country, we were taught to cut the skin and make an X over the bite with a very sharp knife, then the tourniquet above the bite and then have someone suck the poison out. Also told not to run at all or walk very far as this could cause the poison to spread through your body quicker.
Guess it has changed?
A friend of mines dog was bitten by a snake and the anti venom that the vet gave the dog was very expensive, several thousand dollars.
One of my dogs was bitten by a copperhead on the end of his nose. It was many years ago and I don't remember it being a big deal.