No you'll simply kill the plant as suspected but you can get a cutting to last a long long time in a open air fridge at 50-52 degrees with a constant 50 %RH If you wanna have a laugh back at my expense. Try your hand at freeze drying them when there in full bloom.

Miniature roses need no winter protection unless they are in a pot. These roses are on their own roots. I never cover mine and my minis have had temp down to -15 and they lived thru it!
For a potted mini, just move it to a shed or garage. Water it when you move it in.

Thanks for the info, dan keil cr! I covered mine with layers of shredded leaves and compost, but was worried because we have had almost no snow here in Nebraska and it has been bitter cold and very windy. With luck I won't lose any of mine. Didn't lose any last year, but then we had 3+ feet of snow cover from early December through March, so they were well-protected.