We got there very late at night during the off-season, and they had us park for free in their small lot by the hotel. Not sure what high season would bring.
When we went in July, they would charge for their adjacent parking, but they also mentioned that the Vail Parking garage was free - and nearby (~2 blocks). We parked in the Vail parking garage - and would do it again.
Get an answer from Christiania at Vail staff and past guests.