We get snakes in our yard, quite a few of them around my area, open space behind my house. The bull and garden snakes I leave alone, if I see a rattler I kill it or ask my husband to. Years back my dog was bitten in the back leg by a rattler that was hiding in the weeds, I don't think he was even aware of the snake when it happened. He was holding up his leg when I let him into the house. I shaved the area and saw clearly it was a bite.
Soon he started panting heavily and drooling (something he never did), I rushed him to the emergency vet hospital and they gave him some anti-venom, IVs and kept him overnight. Luckily he was okay the next day, never did see or find that particular snake. Like your dogs, mine always kept their distance from snakes.