The writing on the mug, when I was there in December, said that it was only good at the resort of purchase.
However, when I got them at the CR, the CM made a point to tell me that I could use them at the other resorts if I was planning to visit to see Xmas decorations.
When we were at the Poly, GF, and WL, I asked the CM's there if I was allowed to use my CR mug, just to see what they would say, and at each of these resorts, I was told it was no problem and that I was free to use them anywhere during my stay.
So, my suggestion is to ask since it is possible that the policy has been relaxed since the mugs were printed.