MTB the East ABQ foothills, especially the south end (Indian School trailhead, avoid Copper), dries out fairly quickly if it snows and warms up. North end from Spain trailhead has more miles of trail and gets pretty technical in spots, but has more places where shade will cause snowy/muddy spots where snow takes longer to dry out. We usually start seeing more snow in February and March, but even then it's usually not a lot and is gone after a couple days. It's pretty random as to whether it snows or not and how much. Placitas is basically same as foothills, just a little further off (park in the uphill lot, not the downhill lot). Rio Rancho is sandier, better for fatter tires. For the weekends if it's warm enough and hasn't snowed recently, you can go ride south of Tijeras (Park at Chamisoso/Coyote or at Pine Flats) and there's some great trails.
Road bike you'll want to stick to Tramway generally, but some people like to add on from the Sandia Casino towards the river then up north to Bernalillo. You can also ride the river trail, it's paved, but at times it gets busy so you're dodging other bikers and pedestrians/runners. Road biking in ABQ is kind of boring IMO. If it's warm enough then riding east on Route 66 up to Tijeras and south on 337 is a local favorite and more interesting, but don't park near Central/Tramway (high crime/homeless).
I guess I would recommend MTB, gives you more options, but I'm biased.