winter doramncy is definately the best time for fig. That would also be a good time for the orange.
For the orange, be sure to cut back most of the leaf and branches. When you cut enough roots to transplant the tree can't support very much leaf. The tree will sprout new ones soon after being in the ground.
I strongly recomend painting the trunk with white latex house paint the same day as you dig it, even the day before if that is more convinient. It will protect the bark from sunburn.
The fig, if moved durring dormancy, will be far less stressed and will do well.
Keep the root ball moist on both until they are in the ground again. Desication (roots drying out) is the leading cause of transplant failer. Once in the ground, again, keep the roots moist. Remember, the only roots are in the small root ball you moved and that is the part that needs to be keept moist with each watering.
Arthur the Date Palm Guy