Because in Spanish, we use hacer for most weather, so mucho affects the verb, just like "ella corre mucho" is "she runs a lot", not "she runs very" (muy)
because here, "cold" is an adjetive. cold works like an adjetive here.
A lot of wind ( wind here is a noun) or very windy (windy is an adjetive)
This is rediculous! I put "december is very cold" and counted wrong. Literally, it is "It makes much cold in december", so I just wrote an normal way to say it in English.
The stricter translation that is equally natural to say in English is "It's very cold in December". Duo tends to prefer strict translations.