Bettas vary by individual personality as to whether they'll tolerate ANY other tank inhabitants. Some are fine with nearly anything (as long it doesn't look too much like a betta, or isn't big and threatening), and others won't tolerate ANYTHING in their tank!
Mine was fine with Neon tetras and ghost shrimp in his small tank, and no problem with snails. Others have plenty of horror stories to share. So you never know until you try.
Many people have good luck with Nerite snails. They're smaller than some other types, they do a good job on algae control, their tentacles are tiny so the escape notice (moreso than the large wiggly tentacles on mystery snails that often get nipped). Also, they sometimes lay eggs but they need brackish (salty) water to hatch so no need to worry about overpopulation from snail breeding in a freshwater tank with Nerite snails. You can handle two Nerites in a 2-3 gallon tanks no problem.