March is a better time for pruning roses, when you can see and remove any winter frost or other damage. Don't do it now because if we have a very mild winter it could be tempted to start shooting and then be susceptible to a late frost. There is a video showing you how to do it if you google pruning miniature roses. The stems should become more robust as the plant matures anyway.Its still only a baby!

The main issue is the pot freezing and cracking. Any chance you can plant the rose in the garden in a nice sunny spot? Then add a layer of mulch to keep the rootball snug and prevent it from freezing. I usually prune in Spring or late winter after threat of hard freeze because roses usually have some winter die back.