Are there hotels at Copper Mountain?
Pretty much no; there are no hotels in Copper Mountain, depending on how strict your definition of “hotel” is. There are a wide variety of condos in Copper, but there are no hotels, as is Holiday Inn/Best Western/Ramada, etc. The condos are great, and because Copper Mountain has such a small footprint, you will be very close to the slopes.
However, if you strongly prefer staying in a hotel we recommend staying at nearby Frisco or Dillon. Both are just a short shuttle ride away.