Yes, as stated- it depends on what you consider to be 'small.' If you're talking about a shetland or miniature horse, my answer is an indefinite no. Shetlands, though very strong their size, aren't very tall at all, and miniatures are generally even smaller. In fact, I'm of the opinion that they shouldnt be ridden at all. Not even by tiny children. Our shetland is about 325 pounds give or take some, but I'd never put anyone over 60 pounds on him.
If you're talking about an actual pony though, then you might possibly be ok. At your height and weight, I'd say that a stocky pony over 12.2hh would be fine, but remember that you will most likely hit a big growth spurt in the next year or two and will be too large for the pony. For that reason I'd recommend a pony of about 13.2hh because at that size, you would probably be able to ride it without having to worry about outgrowing it in a few years.
I'm sixteen and finished growing (sadly xD) I'm 4'11 and ~90 pounds, and I won't ride anything smaller than our very stocky 11.2hh welsh/shetland pony, especially if doing anything more than a walk.
If you don't have much experience though, what about taking lessons on a horse instead? That way you could learn without worrying about it being too scary or outgrowing it, and you'd be ready for any horse that you might buy in the future?
Everyone in your life is meant to
be in your journey, but not all of
them are meant to stay till the end.