Q.How/when Should A Climbing Rose Be Trimmed After A Catostrophic Trim
It fell off it’s trellis during a bad wind storm this winter, and was trimmed back VERY far to get it back to a manageable size. A bracing fence has been put around it (about 8ft off the ground), and it has been sprouting all over the remaining trunk and branches (it was about 15-20 years old, and went up ~ 20 feet and then spread on the high trellis another 20 feet). It’s sprouting is so enthusiastic, I wonder if I should choose winners and trim some, since there are so many new branches being made, mainly closer to the ground, much fewer higher up. I assume the ones coming out of the ground are from the root, which I assume is not necessarily the same rose as my climber.

Certified GKH Gardening Expert
IF you know for sure the rose was grafted, then yes, the ones coming from the ground are likely from the grafted root. You may want to leave a couple to see what they produce and remove the rest.
https://www.gardeningknowhow.com/ornamental/flowers/roses/pruning-climbing-roses.htm