Only copperhead bitten dog I've had was an English setter that's head swelled up like the Hulk's. Went from white to pink, because the hair was on end. Doc gave him cortisone, anti-biotics and time. (Grandpa used to just give them time.) More recently I've picked up the trick of heavily dosing them with Benadryl to retard allergic reaction to the venom, and seen good results on two of my Chessies and a few friends' and guest Labs that have been hit by cottonmouths.
I keep liquid Benadryl in the truck, boat, shell box and day pack for quick administration and won't hesitate to chug a double dose myself if I get nailed.
If you think I'm wrong, you might be right.