We have timber rattlers and copperheads here in north Jersey, and no recorded case of a person dying from a bite (ever). Usually the snakes try to avoid you (feeling your vibrations in the ground as you approach), but the problems are 1) copperheads are thick, slow snakes - they have a hard time getting out of the way in time - and 2) people rock-climbing reach up where they can’t see, and disturb timber rattlers sunning themselves on the rocks. Many people don’t realize that poisonous snakes can give a “dry bite” (non-venomous); the venom is a digestive aid, and SUPPOSEDLY they wouldn’t waste it on something they can’t eat (because they have to take time producing more). In any case, I think it helps if you keep the bitten area below the level of your heart; I’d also use an “almost-tourniquet” (not completely cutting off the circulation, but slowing it) if I was simply waiting for an ambulance. As a hiker, I have the kit this guy used, and it is impressive. It works like a syringe but sucks, and comes with different sized “suckers” to best match your bite.
I have a nice picture of a reared-up copperhead on the Palisades overlooking the Hudson River; it despaired of escaping and figured it had a better chance fighting.
We have here in my region of California what is known as "The Mojave Green." It injects a combination hemotoxin and neurotoxin. There is an additional problem for victims of that snake's bite in that the proportions of neurotoxin to hemotoxin vary from habitat to habitat. It is best that the treating doctor knows where you were bit.
We also have copperheads in Texas.