I didn't see evidence of mice until I had at least dozen of them living in and under my last coop, they absolutely were sneaking in to eat the spilled feed the chickens couldn't be bothered to clean up. And my chickens aren't smart enough to see mice and say "Dinner!!"
If momma just wanted a place that was dark and cool and safe to have her babies, that's perfectly understandable given the nature of hawks and whatnot. To keep snakes out, the hard part... because they can squeeze through insanely small holes. Every gap bigger than a nickel would have to be stoppered. If your coop sits on the ground I'd check for gaps at the base first, and work my way up the walls at least two feet, more if your guests return. Snakes don't chew through stuff like mice do, so you should be able to use caulking or something similar. As for the chicken door, that's going to be the hard part and if you're really determined you could get a little extreme... if it sits close to the ground consider whether its worth it to you to move it up higher, using a platform for the chickens to come and go.
In the south snakes are an understood risk of chicken keeping and the old boys don't bother keeping them out, just relocate (or kill in the case of venomous ones) them when they do show up. That's your other option, but you may have casualties or lose eggs.
Mice and snakes are why my second coop, the one I'm using now, is up off the ground...