We use animal power for land and timber clearing. Here's the skinny:
Yes, goats will eat trees, but only if their nutritional needs are not met. Otherwise, they mostly eat the leaves and very small saplings or branches (less than an inch). Be sure they have free-choice mineral and aren't left in an area too long, and they won't destroy any of the good timber nor will they debark. During the growing season, we give our goats roughly 200 sq. ft. per goat per day, and then double or even triple that in a drought or fall season. During the growing season, we move them once or twice a week, dependent on the growth, space provided, forage available, or amount of clearing I want done. During the drought or late season, we give them a bigger area with less fragile vegetation (i.e. no saplings I want to keep), and then supplement with hay. You'll get an eye for it pretty quickly, and adjust as necessary. One thing you'll find with any rotational grazing is that there is never a set rule. It changes constantly with the season, the growth rate, the available forage, the number of animals, the effect you desire, etc. Only experience will teach you. FTR, any goat will work. Most folks use meat goats or a cross bred "scrub" goat for this purpose. We actually use our dairy Alpines, so they are multipurpose, and I milk them as well. The only danger is if they have a larger udder, they may get a few scrapes on briars if I am not careful. It's something to consider. I either cut out the briars, or avoid that area during their peak production season.
As far as pigs, yes they do also do great. We raise the heritage red wattle pig, and they do awesome in the woods! Smaller piglets can be used (we have put them out as early as 9 weeks). You would just need something like a portable hot net fence, whereas the larger pigs could get away with a single wire. Like the goats, the pigs will eat what they need to fulfill their nutritional needs. The less area you give a hog, the faster and more effective their work. Of course, this also means the more damage they can cause. If we want a little clearing and what we call "massaging" of the land, then I leave them just long enough to create a visible disturbance of the soil. If I need an area truly cleared, such as an area I am converting into a parking an storage area, then I leave them much longer so that they really root, churn, and then pack the soil, decimate the weeds and honeysuckle, eat most of the roots, and turn the area into an almost concrete layer. It's awesome!
Here's a picture of how it works on our farm: We have honeysuckle, saplings, russian olive, lots of dead wood, and lots and lots of briars! When we moved in, our woodlands were so thick you could not walk through them during the growing season. Our pigs and goats generally work together, just in separate pens, one following the other (safest parasite-wise if pigs follow goats). The goats generally clear all leaves, weeds, and small, soft branches from about 6 ft. and down. When it is relatively clear and they seem less satisfied and content, we move them on. Then the pigs move in. The pigs chew on branches from their back-height and down. The longer we leave them, the more rooting and root-eating they do. The first year, we only supplemented minimally (like a pail of leftovers a day for 2 pigs), which left them hungry and sped the work along. Of course, they were very lean at harvest, but certainly not thin. They will find food, and work harder when hungry. This year, we gave them free-choice feed along with their browse. They didn't work as hard and had way more back fat, but weren't as destructive to the land either.
As far as fencing, we use the temporary electric net fencing all the time around here! Every animal we have has used it at some point. It is awful to install in the woods, and you will make your life much easier if you whack a little trail for the fence first, but suffer through a day of work, and you will sleep better at night knowing your animals won't escape. Single electric lines on step-in posts are much simpler to install, but have risks. The animals need to be trained to them in a secure pen first. Then, goats will be more respectful if you have 3 lines, rotating hot-ground-hot. That usually keeps all but the most stubborn in. The pigs may need 2 in the beginning if they are smaller or less respectful, but once they are over about 100 lbs, one at nose height will suffice.
Hope this helps. I will try to attach some before and after photos later if you are interested. This can totally be done, and the animals are fun and provide food in addition. We love it!