Well, cats have filthy mouths...
I've never seen a snakebite on one of my goats until this year. This year seems truly different in a lot of ways.
A venomous snake bite starts swelling within moments and has an intense burning sensation that causes distress long after the mere bite would. The swelling is at the initial wound first and travels toward the heart along with the normal bloodflow. Non venomous snakebites don't seem to act in that manner, nothing seems to travel toward the heart causing grotesque swelling at the chest. The venomous bite, if not a dry bite, will usually cause a rotting away of the skin and flesh at the wound, at least slightly. Nonvenomous bites don't seem to cause that either.
Some water snakes have acted aggressively toward us, and since they are much faster in the water than we are have been quite frightening at times. But nonvenomous land snakes would rather scurry away than lay in wait. Unless the goats are truly careless, they aren't likely to trap a garter snake enough to cause a bite. Copperheads won't scurry, they want us to leave, but will not willingly leave themselves, so can be easily trodden upon.
Some people here have experience with much more aggressive rattlesnakes. Since I don't, I don't want to talk about how they behave. The ones we have, I'd have to go out of my way to experience a bite from them. Since I don't like going out of my way for anyone, I never expect that to happen.
Hope that helps...