yes, it's fine to prune in January.

I wouldn't risk it in January, not till we see what's going to happen next weatherwise. Any growth that breaks out on its own now will get killed back IF we actually get some really cold weather, but if you prune them now, when growth is burgeoning, it will encourage even more growth to start. And then, if you've already shortened and pruned everything back, you won't have so much to cut back at the end of February, after any cold damage has been caused.

If the weather continues like this (unlikely, from what I've read, but who knows, really, this strange weather is new) up to February, and the forecast then is for more mildness, I'd risk it and do them then.

Agree with Bamboo, especially as a severe frost is forecast for tonight. We're even leaving our grass long, for protection!

I always winter prune my roses. I haven't lost one yet.

if new growth is showing then pruning now will only encourage more growth as Bamboo says.
Like Bathgate, I've winter pruned in the past when there is no growth evident without any problems.

If you are concerned about wind rock damage then shorten the longest stems by a 1/3 and heel in firmly around the base/root stock.

Our weather is so unpredictable I'd leave it until March , just shortening now where necessary- we may yet get some severe frosts.

I'm in SE England, but mine aren't shooting and have most of the old leaves still intact. As others said it's better to wait until early March as a sharp frost would kill any new shoots and cause dieback. And if a very cold March is in prospect, I'd even wait until April as was the case in 2013.

Thank you for these replies. I think I'll prune the overgrown stems that are waving in the wind and leave the proper pruning until March as advised. However I will give a rampant climber the Bathgate treatment where it has become a nuisance!