I am in the Utah mountains and ride all winter. Since we will be snowcovered soon, and not clear until April or later, most of that won’t be singletrack, however. In fact, once the snow flies, I mostly ride my mtn bike on the road, or a few bike paths at lower elevation, and perhaps try sneak a trip south or to lower elevation (winter can be nice in Moab, for example).
I ride at temps down to about zero, or for short rides, a bit below, but the trick is to find warm clothing. Boot covers are a must, as are good gloves. I wear a beanie and ear brassier under my helmet, and underlayers etc from the ski shops. XC skiing stuff works pretty well, I find.
This year, I think I will slap some fenders on the bike though, as it is the slop thrown up from the tires that gets me soaked and muddy, and prematurely cold.
Last year, I managed to ride 60-100 miles per week through the winter, which made one hell of a difference in how well I could ride in the early spring this past year! Work in the gym just isn’t the same!