You can feed some types of snails, but many have shells that are too hard for bettas. If you do want to feed snails only feed those you have purchased (don't find them in the backyard as they could make your betta ill) and only feed them as an occasional treat.
Pellets should be the cornerstone of his diet as good pellets contain many essential nutrients for your betta. I suggest Omega One or New Life Spectrum pellets.
You could also try feeding frozen bloodworms, frozen daphnia, or brine shrimp. All of which can be purchased at many pet stores and local fish stores.