Not usual. We've been down at the end of Dec and January and the weather was the same each time, daytime 80's and not humid, great for swimming and sunbathing.It rarely gets 'cold' there.
Have a look at the Weather Underground site, put Cancun into the search box then about half way down there is segment called History and Almanac. Put in the dates you want to look at and it will pull up the records for those dates. Low temp on the days I just looked at was in the 60's....

I agree with emdia, that is not normal! Whilst you can never guarantee constant sunshine and warm temperatures anywhere at anytime, usually the weather at that time of year is hot enough for sunbathing & swimming during the day but I would always recommend to take a light jacket or fleece for night time or in case of any cloudy days.