Here's the worst-case scenario: I was there during a record-cold spell in January 2003. The coldest night, we had a hard freeze and it was in the upper-20s when we headed to the park, with heavy northerly winds! We had ALL of our "get from the car to the airport up north" clothes on. By mid-day, it was in the low-40s with heavy winds. We were COLD! (And it snowed briefly along the east Florida coast that day...) There was no line for Splash Mountain, though. (No, we didn't go on it...) Ironically, my brother was skiing in Colorado at the same time, and it was warmer for him than for me!
However, cold as that day was, the days around it were cool, but tolerable. We only had one "swimmable" day that week, but most days had highs in the low 60s, and lows in the 40s (and probably still in the 50s by the time we left the park)
Keep in mind that this was a "once in 20 years" cold snap - it's unlikely you'll have similarly bad luck... But you should be prepared if it occurs...
Of course, the same period of time the year before, my brother (same one who was skiing) was there, and had highs in the 80s. So you never know...