It would depend on the rose and on your winter temps. Your main concern would be that the frost doesn't get to the roots of the rose through the sides of the pot. If the pot is small I would put the whole thing in a larger pot and insulate the space between with leaves or straw. Mulch over the crown of the plant and don't worry about the canes. Put it in a sheltered spot. In most of the UK this will probably do the trick. In the spring prune the canes back to live wood and they will come back.

mine stay out. i have one in a large pot and a couple in the ground. the one in the pot gets put in the shelter of the lee of the wall.

I have one in a good size thick pot which I have put near the wall now with other pots around it and hope that will be ok here in the south east.

i would expect it will be fine.