Natalie,
January can be a bit chilly for swimming, though the pools there are heated, so it is certainly possible. The average temperature in January is 61 degrees, with highs up around 72 and lows at 50.
I think that leaving time open for what you described is essential. I think that a dip in the pool on the arrival day is great, as it gets the relaxation part of your vacation started, and it can get kids to calm down a bit. They can get pretty psyched up for the trip, and this tension breaker might be just what the doctor ordered.
I have been there in January where you could swim, and when it was out of the question. I would plan for your trip with the assumption that each day will bring weather that you can swim with, but be prepared with alternative relaxation plans in case it is not. Downtown Disney is a great one, but check out this page of
special activities for other things to do that you might also want to think about.
I hope that helps!
Have a magical vacation!