Your Yucca has great potential for recovery, just have to wait till your conditions are much warmer. As long as the trunks and limbs are staying firm they should do well. It is very efficient in saving the moisture it gets, so be careful when watering, especially when your plant has no leaves yet.
My Yucca has been outdoors year round here, and I have been mean to it really..but it just goes and goes. Our winters are milder though but it is the same time we get some rains.
It also had the middle part go black, almost looks rotten really, but it has healed itself and continues to grow:
