Sean
you are getting alot of info here most of it is good,although i would not recomend " tieing a hog to a horses tail".lol shurely he wasnt serious.
i own and have rode alot of gaited horses, they are smooth as silk on the trail, but they tend to get just as rough as a quarter horse in the conditions you are catching hogs in, rocks, briars, thick brush,ect.
as far as filming from horse back the only way thats going to work is get as close as possible, tie the horse up and walk in.
i take alot of pictures and most of the time thats what i do , sometimes i can get a picture or 2 from horseback but you are going to have to get on the ground to catch the hog anyway so i usually pull my camera out once im on the ground snap a few then catch the hog.
i have rode my whole life and it would be tough to carry a camera with one hand while busting thru brush and make a good video.
the ranch im hunting on now is 14,000 acres and it is loaded with hogs, and a horse is the only way i can hunt 90% of this place.
last weekend my dogs bayed on the other side of a cross fence ,i snaged my catch dog and put her on a leash, tied my horse up and led my catch dog to the bay. it was about a 1/2 mile over a mountian ,caught the hog and walked back to get my horse.
so you have to be able to adust to the situation.
the picture below shows how we have loaded live hogs on a mule.