Cindi ... depending upon what's going on with the roots, I do think it's possible to give them a new start in that both have new wood coming from the bud union ... if I am seeing the photo correctly.
You can cut off dead wood any time, but I wouldn't cut off any top growth of a cane that has life at this time of year because the roses are storing nutrients in those canes. They can be cut back in spring. I have cut back roses I've rescued this way to one or two bud eyes above the bud union and the rose responded with new growth. I call that the do-or-die prune.
Roses don't need light at this time of year. Light is needed for photosynthesis. Growers harvest their roses from the field from late October through November by machine, process them and then put them in dark cold storage until it is time to prepare them for shipping. If you can duplicate the "dark cold storage", you could also bare root them. I am thinking a heated garage with a window is unnecessary at this time of year, but you could go that direction in early spring.
As for next to a stone wall, I've read about people doing that but have not done it myself. So, I really don't know what to tell you about that. Maybe others can give you better information.