Taos Ski Valley has plenty of free parking. Shuttles rotate through the lots and drop you off, and pick you up, at Thunderbird Road near the Village Core. From there is a short walk to Lift 1 and the ticket office.
If you want your vehicle close to the Village Core you can purchase a VIP day parking pass for $20/day or $500 for the ski season. Stop by the parking shack at the end of Sutton Place to purchase VIP parking.