First, welcome to the forum! I'm pretty new here too, but I try to drop in from time to time.
Second, I totally feel your pain. I was homeschooled for a little while, and my online friends were really the only ones I talked to! When I started attending high school & got a job at a stable, I struggled to make friends because I couldn't afford a horse or lessons. I just worked there because I wanted to be close to horses in any way I could, even if it didn't involve riding.
I knew several girls at my school that were into horses, but they didn't like me much. We came from very different backgrounds. That, and several of them didn't like the fact that my mother was married to another woman.
Really, you have to ask yourself if you really want to be friends with these people. If the answer is yes, you should focus on being friendly. People love compliments, and invitations to talk about themselves & their horses. Ask them about their horse's personality, when they got them, and how long they've been riding. They might ask you questions in return!
Don't be afraid to exchange phone numbers and stuff. Once you've spoken enough, offer to do things with them -- whether it involves taking a ride together or getting ice cream. It sounds typical, but I knew a lot of teenagers that wanted to do those things, but felt that they were awkward or cliche. Your interactions shouldn't be confined to texting and lessons/school! Your best friendships will involve spending time together voluntarily.
Lastly, good luck! I'm 19 now and I bought my own horse in August. If you told 15yo me that she'd own a horse in a few years time, she wouldn't have believed it. Since I got Ladybird, I've made two online friends who also like horses. Keep your head up!