4x4 with Severe Snow rated AT's will exceed any requirements, the'll shut the roads down beyond that.
There's forest roads like the one out to CU Mountain Campus in Pingree Park that are "open" all year long.. but thats a relative term, during or right after snow it might not be passable as those are lower priority alternate routes and might not get a plow for a while.. as always use your judgement on those and dont expect a road closed sign on an impassable route.
Once you break away from the ski resorts there's plenty of paved and plowed 2 lanes with great views and little to no traffic.. if its actually snowing these can be thrilling enough but if not they are quite scenic.. if I want to get my snow busting game on I just go out while its snowing and keep on driving past the ski resorts.
Without a bunch more recovery gear (like chains) and a buddy to yank me out, I dont try to venture too far off pavement this time of year.. Wife aint up for those kinda thrills anymore.. I carry a kinetic strap but its seen more use pulling other people out.
This time of year its hard to give recommendations, whats fine today might be deadly tomorrow.. next month, who knows.. if we dont get any snow there could be a ton of opportunities for you, or the opposite.. you might find traversing pavement challenging enough.. thats the mountains in the winter for yeh.