Money is tight for a lot of college students, but it you learn to ride well enough, you might be able to either pick up some cash or to get some free rides - I'm on vacation right now, and I don't want my horse to stand around in the paddock for a week getting lazy and losing his conditioning, so I pay someone to ride him. Not a lot, but it makes a difference to her, and I know that I'm getting him a quality ride and it takes the worry away from me. I know I'm not alone in this, either. A friend of mine who was in medical school (talk about time-consuming and expensive!) still had time to go exercise horses every week for a woman who had a string of 5 or 6 foxhunting horses, and not enough time to work all of them regularly.
It sounds like your mom isn't horsey at all, which is why she doesn't know about these things - don't worry about what is going to happen in the future.
Also, it's difficult right now (14 and 15 are two of the hardest ages to be, I think) but once you're a little older, you could get work mucking stalls and such, and instead of being a "hobby" like it is now, it would be a "job". My parents aren't horsey at all, and they don't really approve of time-consuming hobbies, but they *totally* understood "get a job". So that might work for you in the longer run. At least your folks will get you lessons - mine wouldn't even go that far.
Where there is a will, there is a way.