Anne,
My boyfriend and I just came back from DR last week. We stayed in Punta Cana at the beginning of our trip from Dec. 20 thru Dec. 23rd. It rained almost every day, but we did get several hours of sun and when it was out it was hot enough to get a burn. Because of the high winds along the beach, we spend most of our time by the pool. The weather during Dec/Jan can get a little chilly at night, but I think you'll find great sun tanning weather regardless. Bring a sweater for the evening.
Have a good trip.
Tracy