I agree with spicy food! We went to WDW during a rainy and cold week last December and after two days had to buy down jackets at Uniqlo because we were just so cold. I'd normally say "miserably cold", but we were still at my happy place, so just "cold". The food that hit the spot was at Frontera Grill. We also enjoyed eating indoors for lunch, Tusker House was perfect after waiting in the rain for an hour to go on FOP. Starbucks will also be your friend.
I'd recommend scouring the weather reports and bringing more cold weather gear than you think you need. We are from upstate NY (it snowed early today!) and were so cold because our cozy jackets were at home. We've now invested in layers (think tank top, long sleeve shirt, fleece, crushable down jacket, rain jacket, hat, scarf, and gloves, with running tights/long underwear and jeans) so that won't happen again and so we can peel off as needed. Standing in line is cold work!
PS: We are going at the end of January, too!
January surely can have (relatively speaking) cold weather, but the weather is usually very mild to slightly cool. The mornings might be chilly. Unless we get a cold front, it will be no more than a little chilly. You're smart to come prepared for cool weather, but don't forget your swimsuits, shorts and tees! Happy planning! 
