"It snowed last night."
Heh. I see what you mean. Sounds like a soft-hearted guy who just wants friends but puts up an edgy exterior in some shoujo anime. ...And then he turns out to kind of be a Tuxedo Mask type where he transforms into a magical knight and saves the protagonist again and again but has no memory of it in his usual form. But he's also not the main love interest. Probably owns a black cat.
です and ます are present/future tense.
でした and ました are past tense.
ます and ました are verb suffixes,(降りました is the past tense for the verb 降る [to fall] > it fell).
です and でした are a shortened form of the phrase では あり(ます/ました) following a noun or adjective, meaning roughly "it is" (雪です> it is snow, 寒いでした it was cold).
Although you didn't ask, が あり(ます/ました) means roughly "there is" (雪があります > there is snow).
That wouldn't work because を marks a direct object, the thing a verb is acting on. 降る 'fall' is an intransitive verb, meaning it does not take a direct object. You cannot do the action of "fall the snow".
"Snow" here is the subject が that is doing the action of falling