
Japanese sentence means "It snowed for several days".

何日も doesn't just mean several days.

That's the expression that means EXACTLY "for many/several days": http://jisho.org/search/%E4%BD%...97%A5%E3%82%82
PS: I understand that you use an English idiom for your translation with almost the same meaning... But Japanese expression isn't idiomatic at all. Actually it's just a word from the dictionary.

"For days on end" means "many days", which is also what the definition you quote says.
http://eow.alc.co.jp/search?q=%...97%A5%E3%82%82