No, spring is the right time to do it! This has been a particularly bad winter and there is probably a lot of dead wood that needs to be removed anyway. It may still be a little early yet where you are. I usually start my pruning when the forsythias start to bloom. That is a good gauge for when the ground is warm enough for the roses to start growing.

It's very hard to tell from that picture what it is. There are a couple of possibilities right off hand, Knock Out or Dr. Huey, but we'd need more pictures of the blooms, leaves and whole plant to be more sure. Does it repeat bloom all season or just once in the spring?

Thanks so much for your input! I think last summer it bloomed throughout. Can you give a good resource for pruning roses? I'd like a video, and there are tons out there but I want to make sure it's from a reliable source. Not, gardenpedia or the like :) . One it starts blooming I'll get more pictures.

One other question - the pink roses still have the hips on the tips of the branches. Should I remove these?