The weather is a huge unknown in January. For our December trip I dressed DS in pants, a long-sleeve T with a short-sleeve T over it, a fleece jacket, and hat in the morning (with a pair of shorts in the diaper bag if it was supposed to get hot). As the day went on, we would adjust the layers as needed down and then back up. It worked really well for us. We always arrived at park opening when it was quite cold, but it warmed up a good bit in the afternoons.
I wore pants every day, but packed a combination of short and long-sleeve T-shirts and also adjusted layers. (I did pack a pair of shorts in case it got really warm, but never pulled them out.) We had also packed heavy winter coats in case it got REALLY cold, but didn't those either.