Can you also say "Mi is említjük azt, hogy hideg van"? If not, is the definite conjugation used because the following clause is treated sort of like an object?
You can! Actually, the usual way to think about this is that in the original sentence "azt" is implicit.
That's what I figured was the case. My thought of the following clause being treated like an object was only in the case that 'azt' wouldn't be correct, but that if it was it was simply implied. Thank you for the confirmation on this! :D
There was a good discussion on a similar situation here, you might find it useful: