What we do for winter trips is wear our heavier (and sometimes heaviest) coats on the plane. We generally need them when we leave and when we return to Chicago, so we don't regret having them. We can also use them as extra blankets/pillows/cushions on the plane. We look at the forecast each day to determine if we need to bring the heavy coats to the parks. In January 2009, it was 28 when we arrived at WDW, and the grounds crew was breaking out the tarps to protect the plants from the freezing temps. We were very glad we had our warm coats with us. It was in the 20s at night and the 50s during the day for the first few days of the trip. Luckily, it got into the 70s a few days later, so we were able to break out the shorts we packed. We just left the big coats in the room for those days.
On a side note, I was entertained by how quickly Disney can rotate their merchandise based on need. There was one kiosk at Epcot that was scarves, hats, gloves, and warm blankets on the first day of the trip. When we walked by a few days later, it was sunscreen and towels. They have merchandising down to a science.