I'd agree with the clogged/frozen drains. Best bet is to keep the snow off the roof. The sunroof is designed to pass water through the "seal" and down the drains. If the drains freeze closed, there is no where for the water to go.
If you open the roof, you probably have a nice trough of water up there with no place to go.
You could also run the car with the heat on full and hope that the interior gets warm enough to clear the tubes. Not sure where they run in the 4runner but most cars run them down the A and possibly B pillars.
I had a buddy with a Vanagon that had a huge sunroof and clogged drains. When he would stop, the water would rush to the front of the opening and splash/pour over/out of the channel and give him a nice cold shower.