We have always gone to WDW in January. We are from a cold winter climate so even if it's only in the 60's when we go it doesn't bother us. It feels balmy to us!
I do remember the last time we were there it was sunny during the day, but in the evening it did get quite chilly. We were in jeans/sweatshirts and I was actually kind of wishing I had brought earmuffs and my gloves. It was cold enough we could see our breath. But we still had a great time.