I can't think of a better place to be in January. If you have been in New England in the winter, you know what I mean.
I used to like the cold. After all, camping meant no bugs! Crowds were kept at a minimum and it was real peaceful. But now the cold and dark get to me.
But in the last decade or so we head to an island or Central America sometime over the winter. We could travel in February when I was in administration, but now that I am back in the classroom, my January break is the chance to travel south. (This leaves 3 months of cold crappy weather once we return, but hey, that's the way it is.)
Anyway, how much sun can we expect in Martinique in January? Use a sun path diagram:
http://www.sunearthtools.com
These guys call it a sun position graph.