I just called Fort Wilderness Guest Services and here is the answer they gave me:
"The official answer is NO, guests are not allowed to buy their mugs at FW and refill them at Wilderness Lodge, or vice versa. BUT, we have no control over the individual cast members and what they will allow a guest to do."
So, to answer the OP's questions:
The mugs can be refilled with hot beverages at the Meadows Trading post. They can be refilled with hot and cold beverages at the Trail's End. They "officially" cannot be refilled at the Wilderness Lodge, but if you try then it's at your own risk.
The issue of refillable mugs always is a hot issue. Personally, I buy a new mug every visit and follow the official rules, although I know everyone doesn't see it that way. I have an interesting anecdote re. this issue though.
Last February my wife and I spent a few days at WL. We like eating at Roaring Forks, so saw almost every mug imaginable being refilled. It was all my wife could do to restrain me from making my usual biting remarks as people refilled mugs from FW, Pop Century, and a variety of other mugs. I had to laugh, though, when this guy came in and proceeded to fill an empty bread bag with Coke! I mean, this thing looked like an overfilled water balloon when he left. I didn't follow him, although I wish I had, because I'm sure he didn't make it back to his room, but if he had, I couldn't imagine him trying to pour the Coke out of this bag.