According to the information I have, fig trees do not need to be pruned except in order to be turned into the desired shape when young. If you don't particularly have a desired shape, then you wouldn't need to prune it - which would solve that part of the problem.
If the tree is not dormant, don't put it outside in the cold weather - without experiencing the change of the seasons and going dormant, it is not prepared for the cold. Wait until the warm weather so that the temperature is in tune with the stage that the tree is at.
See this other question for general young-fig-tree care: How do I care for a young fig tree?How do I care for a young fig tree?
