For all of you with Apple Watches, there is an “Equestrian Sport” setting!!!
For your first riding workout, select “other” as the workout option. At the end of the workout, it will give you an option to name the workout, so click that. You will access a huge list of sports and “Equestrian Sport” is in there. After doing this the first time, “Equestrian Sport” should show up right near the top of your list every time you hit the workout mode option.
It bases your calories burned off of your heart rate rather than steps, as others have said, so it’s actually a better and more accurate option than outdoor walk. I know mine seems quite accurate–a quiet meander down the trail garners me way less calories burned than a jumping lesson or a horse show where my adrenalin and my heart is pumping 
Now the bad–I smashed my Apple Watch face the first week I had it. Literally exactly a week. I don’t know exactly what happened, as it was fine and then I was driving in my car and looked down and the face was totalled. The only thing I had been doing before I got in my car was folding up horse blankets. Somehow, maybe, a buckle on a blanket perfectly struck the watch face to smash it completely. Beyond repair. I can’t say for certain this is what happened, but in my experience the faces are stupidly easy to break.
I got the watch replaced and immediately bought workout wristbands (those fabric thingies runners wear for sweat) and my watch is ALWAYS, ALWAYS, ALWAYS covered at the barn now. I like the bands I bought, they are really thin and not bulky, and I can just slip it off the face to check the time or pause my music or turn on workouts or whatever. And it makes me feel a little more secure that there is some cushion between the face and whatever the barn might throw at me.
Take my experience with a grain of salt, but no Apple representative would give me an answer on how durable they are supposed to be, especially since they are advertised as being for workouts and sports, and mine broke when I wasn’t even being active. Apple was super unresponsive and unhelpful overall, and I was pretty upset about it, but I had just sunk $600 into the damn thing so it wasn’t like I had much of a choice. They made me go through the whole process of attempting a repair even though anyone could see that wasn’t going to happen, and then it ended up getting replaced (for a fee, of course).
While I really enjoy having it, I am extremely cautious with it and would suggest others should be too, as it is not cheap to repair/replace these things, even with Apple Care.