I have lots of wooded land on my property. Is there any problem sith fencing off further into the forest for a natural shelter cover? The fields are right next to the trees so pasture would be possible too.

It would depend on the land situation and local laws. Is there a public right of way that goes through the forest? Is the land that part of the forest is on yours, owned, or leased? Would you need a permit to erect a fence in the same way as needing a permit to put up a shed?

I would worry about wild animals in the woods, and I wouldn't put the fence too far in. Enough for a buffer of shelter, but that could be acheived my 10 yards or less.

Minus the laws/rules mentioned I can't see any reason why not unless its heavily lived in by dangerous animals. Especially if you have a nice forest without alot of underbrush so the horses would be able to get in and out easily.

I think that horses have enough instincts to be able to cope in the woods, in the absence of something like cougars or other wild cats in the woods where you are. If the land is yours then I would say that this might make a nice alternative to artificial shelters.

I would just be afraid of them getting too comfortable out there and not seeing much of them!

The land is ours. We own 40 acres. Permits aren't needed here, different rules for city versus country. There's no public right of way at all. In legal aspects it's a go.
As for wild animals, we live on a large island where the biggest wild animal we have is coyotes. And I don't think they frequent our area. The underbrush is sparse too.
It should work. It would be a great natural shelter.

This sounds like the perfect environment for your horse as this is as close to its natural environment as you can get. Is there any chance of the horse getting stolen?

Even if you had cougars you say a large area is not wooded. Horses and other large animals are smart enough to recognize that kind of danger. We have had unofficial cougar siting in our area. One sure sign that it was no hoax was that the cattle stay away from the woods all of a sudden. Wouldn't go near them. Horses would do the same thing.