Most numbered state and US highways in and near the mountains are on good paved road, although a few on the east side are gravel. Few passes cross the range that support highways. Palo Flechado Pass and Bobcat Pass are near Taos, Glorieta Pass skirts the southern end of the range near Santa Fe, and an unnamed pass connects Mora and Peñasco near the middle of the range. All of these can be closed for periods during the winter following snowstorms. Snow tires and either chains have them available but don't use them routinely or 4 wheel drive are a good idea when driving in the mountains between Thanksgiving and mid-March, and on occasion can be needed earlier or later. 4 wheel drive is definitely desirable year-round on some of the minor forest roads, particularly on the west side.
There are a number of roadless areas in the mountains that are accessible to hikers, mountain bikers, etc. In addition to the wilderness areas that are parts of the national forests, Taos Pueblo occupies considerable territory between the town of Taos and the ridge line. In contrast to most roadless areas in the range, the Taos Pueblo lands are closed to visitors without a permit from the tribe which can be difficult to get. There are other private in-holdings at the northern end of the range that may also be closed; check locally. Most areas that are suitable for hiking in the summer are also suitable for cross-country skiing in the winter, but be careful: the ridges are steep enough to pose serious avalanche hazard.