Question
When can I thin it back? Probably dormancy period after winter.  

Can I transplant it during the dormancy period.  It needs more space.  

Answer
You prune mainly in the spring to encourage growth but you prune in the summer to control it. Roses will put out loads of new growth in early spring but summer really slows them down. So when you come to move it cut out mainly the old, grayish looking canes and cut the rest back by a half and water well. Then when it throws out tall canes, simply snip them off during next summer.