We were at AK on January 3. It was cold and rainy all morning. As in 30s and 40s cold. But it turned into one of our favorite days.
Park opened at 8:00, and we (9 adults, and 3 little ones) had FP for FoP at 8:05. We were at the bus stop at AoA by 7:15, and in Pandora, ponchos on, by 7:45. We all rode Na'vi (the only people in line), and loved it -- and not just because it was dry! Then there was a bit of a break in the rain while we took turns using our FoP FPs (and getting rider swaps for later!), so the little ones had a chance to explore and play the drums, and we got some good pics.
We had KS FP for 9:30, and in the light rain, lots of animals were out. After riding, though, at that point all we really wanted was someplace warm and dry. If it had just been wet, we would have been fine, but it was COLD. So we took the train to Conservation Station/Rafiki's Planet Watch. It turned into one of our favorite family memories of the trip. Very few people were there, so the characters (Rafiki, Timon, Doc McStuffins, and Flik) interacted with our toddlers as if it was a private party. We all had so much fun! And the 11-month-old could crawl around where it was safe and dry. The exhibits were great, too. The vet procedure that morning was a CAT scan of a tortoise. We had intended to stay there for 20-30 minutes, but it was a good hour and a half before we left.
We had lunch at Satu'li Canteen, which has rapidly become one of my very favorite QS places in any park, then traded off using the rider swaps for FoP that we had gotten that morning. The rain became intermittent by early afternoon, and stopped by late afternoon. We did the plaza garden dessert party that night at MK. By then it was dry but VERY cold. Still fun!