OP, I did this for a couple years, not as an owner but as a lesson student, and it genuinely sucked. I wouldn’t do it again without owning a car. Even schlepping up to Riverdale in the Bronx (which should technically be the easiest by public transportation) was an absolute shit show.
The best arrangement I had going for a brief time was carpooling with a group of other riders out to NJ. But even that, let me tell you, is no picnic. People are flaky. They make you late. It was exhausting and at times not worth the time saved compared to taking the bus. Plus I still had to take the subway 30 min just to get to the home of the car owner, then stand around in her apartment while it took her forever to get out the door! Omg I would never put myself through that again…
The reason public transit sucks so much is that, while it’s predictable, it can be JUST unpredictable enough to screw you over. And the longer the commute, the more that effect is magnified. Sometimes everything goes smoothly and operates on time—no sick passengers, no “train traffic ahead of us,” no changes to bus service meaning we blow half a mile past my stop—and the “reward” is you show up thirty minutes early and get stuck waiting around for your lesson time. But if you don’t leave home early enough to account for those little unpredictable incidentals (and sometimes even if you do) you’ll be incredibly, unforgivably late.
Also, another limiting factor is that, while the public transit may get you within a 5-mile radius of your intended destination, those last few miles can suck. You call an Uber, it can take anywhere between 5 and 20 min to get picked up, you’re out $15, and you have to repeat that on the way back—Uber to train (or bus), train to subway, subway to walk-up…
If I were you, I would leave my horse in Europe…