Tbh, I’d just text her. Something nice and thanking her for all the work she’s done. “I’ve found a barn closer to school that’s going to work well with my schedule this year.” Another thanks at the end, and that it. Super simple, happens all the time, and you’re not pulling a horse or dropping a lease.
The fewer details the better. Don’t talk about focusing on school and then go post on social about buying a horse and riding every day. Trainer won’t care or notice, probably, but honesty is better - and being vague with the details is best.