from the 23rd of dec through to the 6/7th of Jan most operators dont run tours in Uyuni as the drivers 1. need a holida like anyone else and 2. Many cant be trusted to not drink. 3, Even if they can be trusted not to drink they cant guarantee they can avoid being crashed into by another drunk driver.
There will be a hand full of operators that think , hey great noone is selling tours we can make a killing here, and run the tour regardless - these of course are not being very responsible usually and just after the $$$.
I always tell the many inquiries we get about tours over this period that if you MUST do a tour then it is best to stick to a one day tour as it is far less likely that your driver will end up drinking on a one day (he can go home and drink after the tour if he wants) . On a three day the drivers will probably end out going to see their friends in the nearby village that you are staying and get wrecked , then waddle back at 5am in no state to drive.
Christmas itself in Bolivia tends to be very much a family after so christmas day everywhere is pretty dead , best place for travellers is usually to stay in a hostel that is putting something on for Christmas (if thats what you want to do of course)