Like many things in life, the answer to your concern is, "It depends." Specifically, it depends on the size of the dog, the size and species of the snake, and a particular dog's sensitivity to the venom. Where I grew up (LA), it was very common for Labs/Chessies to get bitten on/near their faces by Cottonmouths in the marshes. Many, and if my memory serves me well, most survived, even without antivenin.
I'd do it if I were you. I don't think Cottonmouths, or Copperheads generally would kill it, BUT a rattlesnake could do so easily. That's the main reason I'd do it. My uncle's been doing it for years with his bird dogs. You just can't take chances with those rattlesnakes. If it was to bite them in a bad spot you might not have the time to make it.
Here's a follow-up on the question of Benadryl dosage. The fellow I emailed basically had this to say. I'll paraphrase:
Diphenhydramine has a wide margin of safety, and the lower dosages (50mg for a large dog, for example) are appropriate for treatment of atopic allergies such as pollen or grass. The larger doses that I mentioned in my previous post are appropriate "specifically for insect stings where a significant amount of swelling, pain, or inflammation is present. For brief periods (1-2 days), diphenhydramine is very safe at these doses, although side effects may include mild sedation.". The larger dose of 4mg/lb is appropriate only for the bites of pit vipers, and not any other situations.
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