The answer to so many gardening questions is “It depends!” But, in general, frost probably won’t cause lasting damage to your rose bushes, provided you take some precautions.
Mulch around the base
For more details about winterizing your rose bushes, see How can I take care of rose bushes in the winter? For most modern roses, you want to mound some mulch up around the bud union (assuming there is one). Most modern hybrids are grafted onto a rootstock and so, you need to protect the graft or bud union from freezing and thawing, which can weaken or even split the graft union. The more severe winters you experience in your location, the more important it is to cover the base of the rose bush.
Since roses go dormant in the winter, there’s not much damage that frost will do to the rose canes. Of course, you can prune any damage from the canes in springtime.
It’s really a question about when to prune
The main worry about frost tends to come up around the transitional months between fall and winter and then again between winter and spring. Most of us like to wait until after the first hard frost to prune our rose bushes because a hard frost will get rid of most of the leaves. This makes pruning that much easier. Because we tend to get strong winds in November and December in the Pacific Northwest, we like to perform a preliminary pruning in the late fall, just to protect the bushes from wind damage.
We take on the main pruning tasks in the spring or late winter (again, this depends on your particular weather). As the sap starts to rise, roses will put out new growth. We prefer to do our hard pruning before this happens. If we get another frost after this spring pruning, it will cause little to no damage. Of course, there is that rare occasion when we get a week of warm weather (promises, promises), which confuses everybody and every growing thing. If we get a frost after that, there may be damage to any new buds that started pushing out. You just have to prune those damaged buds off and force new growth below the damage.
Check with local experts
Roses are such hardy plants, that there is little to worry about when it comes to frost, as long as you take some basic precautions, as mentioned before. If you live in a severe weather location, you may need to employ more drastic measures, such as piling mulch in a large mound over your bushes. If you do live in a place with extreme weather conditions, search online for “winter rose care in Minnesota” or wherever you live. It’s very likely that you will find local resources, from a regional rose society to your state agricultural extension office, that will tell you exactly how to prepare.