When DH and I go to WDW, we always go in January. Never crowded, and the longest we've waited for any ride is 10 minutes, no need for Fast Pass. The last time we were there we took advantage of E-Ticket night, very un-crowded!! We were allowed to stay right on Big Thunder Mt. Railroad and ride again as there was no line for it. On Pirates of the Carribean DH and I were the ONLY riders in the boat!! It was great!!
The hours of operation are shorter in January, but since you don't wait in long lines it really doesn't matter that it closes earlier than at other times.