I've been dealing with low back pain and it is not recommended. I still wanted to prove I'm capable of running, so my longest distance was 10k and had 2 competitions as well, which I'm proud of. But then my body started to signal and had to take it seriously.
10'C is perfect for running. I've been testing myself and the lowest temperature for me was -5C and I loved it.
Sounds like you have been running! Which in my mind makes you a runner!
Christopher and Eric talk about how fixing running form fixes multiple issues in our bodies, one of the top five being lower back pain. Obviously, I have no idea how bad your pain is and if running is safe for you or not, so I totally trust you'll keep doing whatever makes sense to you and please know there's stuff in their book specifically about lower back pain and running and form.
Running in -5'C!! I haven't done that. The closest I've got, I think, is running at 1'C with a wind chill factor that dropped it to -3'C for a parkrun in our Snowy Mountains here in Australia a few years ago. Cold, cold, cold!