Given your location the direction of exposure is going to be critical. Mel lives in Florida.
If you know which way is the prevailing wind you probably can block that out with a tarp, so long as that isn't southerly, which is where the sun will always be. It will get lower and lower in the sky as the winter solstice approaches.
If it is forty degrees or above, with little wind, and the sun is out and the wall is south facing it is just fine for climbing. We are out there the whole day. You always have your hand in contact with the rock. On the north side, it doesn't matter how many layers you have on, it is just miserable.
I also work on my yard all year long. Working on the north side of the house (3 stories tall) is no fun at all during the winter. So, exposure makes a massive difference once the air temps starts dropping.
You ought to be able to rig a mirror so you can look at the cage. The curved ones have a wider field of view. The mirror could be mounted to the fence or a post. The curved mirror allows you to see around corners.