Hydrangea. Can't name the species.

I wouldn't do anything until they start growing. Then trim off the parts then known to be dead, then any shaping as desired. Each remaining stem should be pointed in a good direction, and end with a strongly growing nub of foliage.

Thank you both! I suspected hydrangea in the first photo, so I immediately told her to wait on pruning it. Do you think both are hydrangea?

Yes. In fact I thought the pictures were all of the same plant.

Happy to reply. Enjoy!