You could easily kill the grass/weeds and not the trees with Round Up. I would think if the area needed any grading, you would compromise the health of the trees. Depending on the type of tree you may be able to just add footing over the ground, depending on how much water it holds, drainage etc. Some trees cannot tolerate having their roots covered or the traffic that alot of riding might cause. I had an area at my old house that had wonderfully draining soil in a wooded area (picture 80 year old oaks that had been thinned out). I was able to ride and set up a small jump course under the trees and could ride in the middle of the day even when it was 90 degrees in the sun. I miss it very much.
I would talk with an arborist to find out if the trees could tolerate it. Then I'd call a contractor. You'd likely need one that has a small skid steer to move the material around in tight quarters.
Upperville just put in all weather footing. I think they left grassy areas at the base of the trees, but excavated around the rest of the arena, laid base, and put in footing on top. Some tree species will be fine with this, others will not. Since the oaks there are so well established, they might be OK. What you need to be sure of is that you're dealing with tree species that can handle soil compaction on top of their roots or are very deep rooted. Oaks tend to be fairly deep rooted, but establishing them in compacted soil can be difficult. For a good guide, look to the tree species that are living in the cities near you. If they can live on a city sidewalk, surrounded by concrete, they can survive a riding arena.
Foxtrack in Southern Pines has huge old trees (oaks I think) in a sand area which they use for warmup at their shows. It is AWESOME in July/August. Of course you don't have to "put down" footing in southern pines.... you just scrape off the grass, and voila you have a sand ring.....
Raises hand. I have two huge cottonwood trees in one half of my arena roughly in the center. Luckily one end is large enough for longeing and only one time has a horse bulled enough to go around the tree (longe person runs fast, really fast to get around tree also). It is lovely in the hot summer to halt horse in the deep shade, and at 5 pm the whole thing is shaded..
I did not start with wonderful footing in there (even though footing is part of my business) because of the trees.. Over time, I have spot fixed and added crusher fines (stone dust), squeegee, used shavings in winter (not manure) and sand to the clay base on one end and the sandy silt on the other end to arrive at pretty good footing after ten years. Unfortunately I cannot add anything to defost the footing in winter also because of the trees, so that is where the used shavings come in because the arena is also my sacrifice turnout off the corrals.
Lucky also that horses do not want to chew cottonwood tree bark. It must taste REALLY bad because one corral also has a huge cottonwood tree that is untouched. The willow trees they can reach are toast.