I would prefer it if it stopped snowing.

This is a second conditional sentence.

I would prefer you to be on time. (= I want you to be on time.)

I’d prefer to stay at home instead. (= I’d rather stay at home.)
I’d prefer to have gone by tram. (= I’d rather have gone by tram. /  I’d be happier if I had gone by tram.)

Note the difference between the sentence above and this one: