Make sure that your storage area has excellent drainage. Roots will die if exposed to wet conditions followed by freezing conditions. The previous comments are primarily for hardy trees. Tropical trees require special attention. Alternatively place your trees under florescent lights.
Most members have an insect problem with their tropicals.
As winter progresses more and more flying insects appear. Last year I used a systemic insecticide when I brought the trees indoors. There was a substantial reduction in the insect population. This year I am applying the systemic in mid September. I will make another application when the trees are brought indoors.