I found this list that describes the temperature in January of popular honeymoon destinations. Thought it might be helpful!
Bahamas - Dry, with highs of about 78 F. Miami - South Florida weather in January is usually quite nice, with some clouds and temps in the high 60's F. Cancun - Sunny with average highs of 81F, cool in the evenings. Hawaii - Average 75 F year round. Watch out for February, though, it is the rainy season. Aruba - Sunny and about 82 F every day. The rainfall occurs mainly in short showers during November and December. Virgin Islands - During January the temperatures in the Virgin Islands typically vary between a daily high of about 84.0 degrees and a daily low of approximately 73.0 degrees Bahamas - Weather varies here (some use the word 'Unstable Weather') but in general the temp is 62-77 degrees. June-November is the official hurricane season, so that shouldn't be a problem in January.