This rosebush was trimmed back last year (2013) from an immense bush that had been neglected by previous owners for years.

After I trimmed it (it was ~3-4 feet high) it bloomed like crazy on all the branches.

This past winter was brutal, lows down to -35F.

This year, looks to me that the old bush part has died and new bush stems are coming in. I started to prune the old busy back to it's main stems, just to get the dead stems out of the way, but should I just try to cut it down to the ground and let the new bush grow?