I doubt you have done any long term damage to the rose at all. Most miniature roses are more frost hardy than "normal sized" varieties. Burying it in a snowdrift for a month wouldn't do it any harm.
The only "problem" is that your rose has been forced into bloom out of season, and you have just reminded it that this is really the middle of winter, and it should be dormant with no leaves or flowers at all, waiting for longer and warmer days to start growing again in about March.
There probably isn't much you can do to keep it in its unnatural "forced" state if you have kicked it back into its normal annual cycle, but if you want to keep it for the long term, put it somewhere cool in the house, don't over-water it or give it any liquid feed, and just wait till it starts to grow again later in spring. Then put it outside for the summer.
It might not flower much this year, but it should be back to normal for summer flowering in 2020.