Nice art, and the animation is a good effort, I have not had much experience myself with animation, in particular pixel art. The others have great suggestions, but I might also suggest rather then having the head go side to side, have it go up and down, as if the snail is using the weight of its head to help it push itself along. I know this is meant to be in a cartoonish style, but I think perhaps some of the problem why it looks odd is that snails would not push themselves along this way in reality. (like a head "scooping" motion", rather then "dipping"), but without exaggerating the animation, have it subtle.
Anyway good work so far , keep it up