Stumps are a pain. And not only will they leave stumps, but they will also leave branches and other debris. It is a huge mess to clean up, so you may want to do what others have suggested and have a company do it all just for the wood. Not sure you'll have luck finding a company willing to do that, but you can try. It varies a lot from region to region, and of course it depends largely on the species and maturity of the wood (I own an 185 acre woodlot). When lumber companies are done clear-cutting, you can't even walk over the areas they've cut because there is so much debris left. It will not rot in any kind of decent time frame either.
The other thing you'll need to think about is erosion and run-off as a result of clearing the property. There will no longer be anything holding the soil in place. In fact, when you remove stumps, you'll find there are a lot of holes left. You'll likely need to bring in fill.
I have been eyeballing a tiny piece of our home property to put in a proper riding ring, but it would have to be cleared, cleaned up, and filled in, and frankly, even just for enough space to put in a riding arena, it's too expensive for me. The trees in there are mostly junk (a little cedar with a lot of poplar) and not old enough to be worth cutting. It may be different there, just make sure you have some solid financial numbers before purchasing the land (in other words, get a company out there for an estimate, and plan on bringing in layers of fill after they're done).
Even leaving some trees in there is possible, but will require a lot of work. You'll want to limb them flush with the trunk so horses can't poke themselves with the branches, and you'll have to check fencing practically daily because trees and branches will interfere and fall on the fence line. I have a handful of trees I've intentionally kept in my pastures, but overall, I prefer to use clear land. Trees are a PITA near fencelines if you ask me.