Yes, though not all roads are open to cars. You can drive into the park through the North Entrance year-round. The winter season of services, tours, activities, and ranger programs typically spans from mid-December to mid-March. At Mammoth, you can take self-guiding tours of Fort Yellowstone and the Mammoth Terraces, join a guided walk or tour, cross-country ski, snowshoe, ice skate (sometimes), rent a hot tub, watch wildlife, attend ranger programs, and visit the Albright Visitor Center. Visitors may legally soak in the Gardner River where hot thermal water mixes with cool river water. You can also arrange for oversnow tours to Norris Geyser Basin, Old Faithful, and the Grand Canyon of the Yellowstone River.
yes
yes