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I was thinking about what's helped my wife the most at the gym. As you say, a strong core is key. For most of her exercises, she started with 3 sets of 12 and gradually worked down to 3 sets of 4 over several months. I suppose horizontal rows, lat pull-downs, the back machine, and the Roman chair have been key. The back machine she started with 1 set of 30 and gradually moved to 3 sets of 12. Roman chair she does with bent legs and just one set to exhaustion. She also benefited from the usual dumbbell work: curls, bench presses, incline presses, bent rows, shrugs, and seated presses. I think you could do such upper body work without affecting your horse work so much.

Lower body, she does barbell squats, one-legged leg presses, and standing one-legged calf raises on a Smith machine using a toe block. https://www.youtube.com/watch?v=qPWXdq7idrI in case you don't know what that is.