January is a time when there could be very rough conditions on the north side of Little Cayman. The big draw on LC is the Bloody Bay Marine Park and Jackson's Bight on the north side of the island. When those are too rough to dive safely or comfortably, the sites on the south side are fine, but are not much different than what you would see on Grand Cayman or a half dozen other places in the Caribbean. The next question is "how often are conditions like that". A good source is to go read the Cayman Aggressor's logs for weeks in past Januaries and see which weeks they skipped the crossing to LC and CB. That is a good gauge on how often the conditions were not suitable for them to dive the north side of LC, since that is where they typically moor if they come across.
With that said, somebody will come along now and tell you that they had a fabulous trip to LC X years ago in January and that the conditions were marvelous. That may be entirely correct as well. There will be days and weeks at a time when conditions are in fact perfect in January, but from mid-October through February, there will also be days and weeks at a time when they can't dive the north side of the island at all. If you are just looking for a great vacation, by all means go. But if you are going specifically to dive the Bloody Bay Wall, winter is not the time I year I would choose to maximize my chances of diving it all week long.