I've cruised twice in January (beginning of January as well) and noted the Christmas theme was completely gone. This was on both Carnival and Princess.
I've found January is a terrific time to go as the weather is generally nice (usual for Caribbean), the crowds are slightly less than Feb/Mar and the prices seem lower. Also less chance of a kid-filled cruise which we prefer to avoid.
We've got one on our radar for Jan 07 as well actually.