Good day all,
Interesting stuff ... But usually these "weird" (or out-of-season) systems don't mean the upcoming main season would be busy or not-busy.
This system is more of a mid-level / semi-subtropical system, and has happened many times before in that part of the Carribean. As of now (Feb 6), the convection is highly displaced to the NE of the surface trough and the system is becoming more of a trough than a closed low.
As for the upcoming season, the warm winter may give the Gulf of Mexico a "head-start" heat-budget wise, but keep in mind that the rest of the tropics is rarely touched by cool air / fronts anyway, regardless of how bad the winter is in the mid-latitudes.
Ofcourse, if there is an active subtropical jet, like 2010 and 2011, nothing would form over the Gulf of Mexico anyway due to the high shear, and anything east of the US would also be weakened and / or recurve out to sea.