in my experience, keeping newly rooted cuttings growing through the winter is possible if what you are growing are roses that don’t need dormancy and if you have enough light. I’ve never grown gallicas or species roses that need dormancy, so I can’t comment on those. I tried growing my cuttings through the winter with the orchids and it was not nearly enough light. The plants became very etiolated. I moved them to the cool garage so that the plants would go dormant, in a partly sunny windowsill. That worked much better for most of them, as the cuttings went into stasis for several months, and then burst forth with growth when brought out in the spring. One rose didn’t do well, with leaves dropping. On subsequent trials, this rose did better leaving it out in the cold over winter (I’m in zone 7).

https://www.purdue.edu/hla/sites/yardandgarden/extpub/new-plants-from-cuttings-text-only/

Above link explains that rootings grow leaves when the air is warm, but zero roots. In contrast, rootings don't grow leaves in cold air, but grow roots if a heating pad is used below. Growing leaves through winter IS A DISADVANTAGE SINCE: water loss is through leaves, above link talked about trimming off leaves to converse water to make roots. Growing leaves in winter also invite spider mite due to warm & dry indoor air.

Agree with Noseometer that keeping rootings DORMANT in cold garage is best. I'm in zone 5a, and tiny rootings (with few hairy roots) survived through winter if kept DORMANT in dark & unheated garage. One winter I stored them down the cool basement, but the gas-heating system kept kicking on and DRIED OUT the soil. it was a nuisance to water them daily, then they died since the leaves got dried out & dropped with dry basement air.