Well, it wasn't "everything freezes to death" like generally assumed would be the case*, but at BEST it would still be catastrophic because Celestia's overthrow and the sun's disappearance/destruction would've overturned all of Equestrian society and probably lead to much death and destruction before the situation could be stabilized by Nightmare Moon and her forces.



*And really now, why would Nightmare Moon want to rule over a frozen wasteland? She wants subjects to "praise her night" - that's the whole point of why she rebelled in the first place!