Most herbivores will eat branches in the winter, they are more nutritious than fallen leaves. Rabbits seem to like some roses better than others - Champlain at my old house always got mowed down to the snow line by rabbits. I guess varieties with less prickles are more attractive, but rabbits don't have too much choice this time of year.

Yes, most likely Rabbit.
The last several day's I have a motion camera set up and I might see
who is nibbling on my stuff. I know it was a Rabbit and eating about
everything what's poking through the snow, including Cotoneaster.

Konrad