Have you ever spent the day in a skid steer? Of everything I've operated, nothing is more painful then hour and hour of running a skid steer. The thought of driving one over open country is so terrible that if I had a skid steer, I would probably just leave it parked and get something else.
I think that a good sized tractor will accomplish most of what you want to do. I also agree with the others in suggesting renting an excavator to get rid of the trees you don't want. If it is going to be a long term project and renting turns out to be too expensive, you might look into buying a full sized backhoe with a 4 in 1 bucket. I have an older New Holland 555E that I modified to accept Universal Quick Attach implements. The grapple is on there more then anything else. At 80 hp, the backhoe will take out any sized tree and the grapple is strong enough to pick up most of them and carry it to the burn pile.
It's one thing to get them out of the ground, it's another thing getting them to the burn pile.
I also have a 170 hp dozer that I've used to clear trees. It's kind of fun at first to push them over, but it doesn't take long to create a huge mess. And when the ground dries up, some of those same sized trees that pushed over easily start to snap off, leaving a stump to dig out. It will also take out any sized tree, but you have to do a lot of digging to cut the roots and build up a ramp to get those bigger ones out. The backhoe is much faster on bigger trees and when comparing the time it takes to clean up a days work on the dozer taking out trees to what you can do with just the backhoe, I've learned not to use the dozer for clearing trees.
Dozers are for pushing dirt.
Eddie