When it comes to camping on snow, you probably won't find anything very clear other than the yurts and the well traveled trails. So just go hit one of those and then tromp off and setup your camp. That's the beauty of snow, it doesn't really matter where you setup camp (just be mindful of where your coals end up). One other thing to consider: 6 miles in the snow has a tendency to feel like twice that on a regular dirt trail. Might want to consider doing a test run a mile or so out. In the winter, that's not much different than being 10 miles out when it comes to solitude.
If I were you, I would head to the Uintas. There are some good trails just outside of Kamas on Hwy 150. Yellow Pine, Shingle Creek, Norway Flats, North Fork Provo River, Upper Setting Road, etc. There's some other good stuff on the opposite side of the road from Shingle but I can't remember the name of it. The area on either side of the North Fork Provo might be one of the best options. There is a great trail that is flared with snow markers that leaves Hwy 150 just down canyon from the bridge over the river. It passes by the Beaver Creek yurt and does a loop, but you could break off anywhere up there and find a place to camp. Perhaps the best thing about that area is that it is wider and flatter than many of the other options so it is probably safer and more forgiving for a first timer camping in the snow. And easier to find campsites too! I have a couple trip reports each on here for Shingle Creek and North Fork Provo, but they weren't in the winter so they might not help much.
This is where the start of the North Fork Trail I'm talking about starts:
https://www.google.com/maps/place/40°35'54.0"N+111°05'55.6"W/@40.598327,-111.099749,536m/data=!3m2!1e3!4b1!4m2!3m1!1s0x0:0x0
There is another trail on the other side that would probably be great too. It's a road for a while but I'm sure it's just a trail in the winter.
Oh, and be sure to stay away from steep slopes and know the avalanche risk. It's not just backcountry skiers that get in trouble with that.
https://utahavalanchecenter.org/
Now with all that said, camping on snow sucks. Go to the desert!