I usually prune my roses at this time of year. Not in icy weather though.

As regards to the cuttings I'd probably wait until spring is properly sprung before potting on or planting them in the ground

Depends what variety or rose you mean - so long as its not ramblers, do them the last week of February. And no, it won't damage them if you cut them - in fact, they'll thrive on it. Remove all weak, dead and diseased wood, and crossing stems which are rubbing together, first, then prune what's left as needed.

Hello masie ... I always cut my hybrid roses back in early March, regardless of the weather. They will be budding nicely by then so it is easier to cut back to the bud. If the weather suddenly freezes then the sap will be rising so there will be less die-back. If you are cutting back a rambler you can be quite harsh and hedge trim it, though I usually do this in late summer/autumn when flowering has finished. About your pot cuttings ... when you gently tip them out of their pot, if you have good strong roots down to the base then re-pot them on in a rose/shrub compost with a dressing of bone meal and wait for further root growth before planting out. Keep them cool, even cold, but do not bring them indoors at this time. Hope this helps.

A good strong root base is important to create a future stronger plant. If they are still potted in spring without showing too much strong root growth (keep checking!) then try a bone meal feed to strengthen root growth.