I think the question looks very different if you are on your own land or in a boarding barn.
If you have land, good farming practices and good land stewardship are by definition environmentally positive. You don’t want fecal runoff in your well water. Etc.
When you board a horse, there is less scope for action. However barns these days tend to have good manure management strategies in place.
The thing I cannot avoid is the amount of gasoline in the background. My hay is brought in by truck from another region by the hay dealer. The hay is baled by machinery. I spend a fortune on gas when I trailer out. I live close to the barn but many folks drive across town to ride.
If I lived on my own land near trails and kept my horses on pasture much of that gasoline consumption would not be there in my footprint.
As far as “sustainable” consumer goods, I tend to avoid that marketing ploy.
Leather as a byproduct of the meat industry makes better gear and is not plastic, unlike the vegan gear.
I buy my breeches on discount and am limited to a few brand models that fit my adult body, so unless that brand had my model in my size in a color I wanted and at 50% off the claim to be organic or whatever wouldn’t move me. I buy all my tops and jackets on sale in general sports stores.
Hay in general is not a crop using high inputs of pesticides, in part because the profit margin is fairly low. So I am not out there sourcing certified organic hay, which incidentally is about $700 a ton here.
So I have to say that while I think about it, I don’t do anything active about it. I also have a long commute to work.