YES they climb roses ! During the winter months, in my garden, they ate every shoot on all of my roses and only left the main canes.
Initially, I thought what I was seeing was deer damage, but I've got all of my deer fencing up to 8' tall, now, and I was still seeing damage every morning.
After they finished eating ALL of the shoots, they started taking down the major canes.
There is NO way a deer can get into my house pad garden. The roses out in front of the house are well protected by deer fencing and the dang rats climbed the fencing to get down into the roses.
The roses will be fine. All it meant for my garden is that the canes are more exposed to the elements and I am seeing more winter damage. I've had to do a harder prune than in the past.
Those small shoots / canes / branches actually provide protection for the main canes and buffer the impact of cold winds and frost. They do not store many nutrients for the plant, those are in the main canes. When those main canes are winter damaged for any reason, it does stress the rose.
However, if the rose is healthy going into winter, it can recover and still be a vigorous plant as long as there is no additional pruning during the winter months.
With the main canes of the roses almost striped, the woodrats went on to eat other things in the garden.
Nature has pruned roses by the teeth of animals for a long time ...
I have found that the rats are not eating the new growth, so I am guessing it is more of a winter feeding habit. I can't find anything on line that tells me that they change their eating habits with the seasons, but it only makes sense.
One of the things I read early on is that they do love woody plants ...