We have a cabin in that area so I'm pretty familiar with it. Hwy. 190 is typically clear up to the Ponderosa, which is a few miles north of Dome Rock. I say typically because if they've had a recent storm, you'll have to wait for the snow plow, though they plow regularly. The two primary places you can stay are Camp Nelson/Pierpoint Springs, which is about 25 mins. down Hwy. 190 or Ponderosa, which has a B & B and a few cabins for rent. Lots more options at Camp Nelson, where there are a lot of vacation homes you can rent, a motel (not swank) and a nice lodge that rarely seems to be open.
Lots of good snowshoeing that time of year. You can pretty much go anywhere from Ponderosa: down to Dome Rock, fire roads, Quaking Aspen, etc. From Camp Nelson, you should be able to hike pretty much anywhere, though you can easily drive up Hwy. 190 to the snow if you want. The Camp Nelson Trail is nice. You can head up toward Sequoia Crest and snowshoe to the Stagg Tree, the largest Sequoia on private land. There's a good sledding hill on the hike in. Most of the time, we just go up there a hang together, play board games, take short little hikes around town, etc. The kids always cry and scream when we leave to come home. You can pick up a local hiking guide at the restaurant in Pierpoint Springs.
Check with Mountain Real Estate (slatemtn.com) or VRBO for rentals. Have fun. You can email me if you have any more questions.