"Ten below", "ten below zero", and "ten degrees below zero" all seem natural to me (BrE speaker), but I'm not sure about "ten degrees celsius below zero". That strikes me as an attempt to shoehorn units into an ambiguous* idiom. It doesn't work, and "-10C" or "minus ten celsius" would be better, in my opinion.

* Both F and C are used in the UK, but I think it's an age divide. I doubt many people under around 40 would use Fahrenheit as their measurement system of choice. I'm 35 and I have no intuitive understanding of Fahrenheit temperatures.