Somewhere east of Cable, WI, is a hike in "wilderness area" that may be open for horses. I'm not sure that it is, but it might be worth checking into. I wanted to do a backpack trip into it when I lived in Wisc but never got it done.
Another option would be the State Forest in Vilas County over on the east side of the state. It's closed to most motorized use which means that beyond a few hundred yards from the paved roads it doesn't get used much at all. It's been logged in the past so there are a bunch of old logging roads you could ride. At least, there used to be a bunch of them. I think there's a good map of the Forest if you contact them. Seems like it's called the American Highlands and Something Or Other State Forest. But I can't remember the name for sure.
Last I heard, the Nicolet National Forest in north central Wisconsin was still closed to most motorized use. Again, it's been logged in the past and there should be a ton of old logging roads you can ride. If you contact them (or check their website) you can probably get an access map that has all the major, minor, and almost non-existant roads and trails on it.
If you draw a line from LaCrosse to Wisconsin Dells and on across the state, north of the line you need to check to see if ATVs are allowed on county forest land. South of the line it's a pretty sure bet that they are not. So, county forests in the southern part of the state might be an option. There are not as many as Up Nort, but there should be some.
If you want to travel to mountains I'd suggest the Black Hills in South Dakota. They are 10 hours from Hudson. Not sure where you live, but that'll give you an idea of distance. I've done a ton of ATVing in the Hills and know many parts of them quite well. The recently changed the ATV rules and the Hills are now much more restrictive--bad of ATVers, good for equestrians. There are some heavy use ATV areas you'd want to stay away from but there are also a million or so acres that don't get much ATV use that would be a great horse camping area. If you're interested I can get out the maps and give you some ideas of where to go. The Forest Travel map is available on the Black Hills National Forest website. That will give you a general idea of the areas where ATVs, motorcycles, etc., are legal but won't tell you where they actually are used. I might be able to help with where they are actually used.
Hope this helps!
"Don't just feed it! Ride it!" And the People said "AMEN!"