I would guess that snake hunting would fall under the varmint regulations and since the only snakes that might make the roads dangerous at night are the two legged variety, I don't think you have too much to worry about.

Truth be told, I've never heard of any snake hunting regulations of any kind, either.
BTW, the prairie rattler, which is the dominant pit viper species here, are so shy and non aggressive, you rarely see them, let alone have to kill them. The Wetern diamondback is a little more aggressive, but is much less common. I've covered nearly every part of NM and while over the years, I've seen a fair number of snakes, given the fact that they are great varmint controllers, I almost never kill them. Also given how much time I've spent hunting and fishing NM, I think you're going to find it more difficult to find the snakes than you think.