Are you sure it was the same circumstance?
雨が降ります。(ame ga furimasu)
It rains. (talking about weather in general, as in "this is a place that gets rain")
雨が降っています。 (ame ga futte imasu)
It is raining. (current condition)
So in the case of this sentence, the difference is the same:
雪が降ります。 (yuki ga furimasu)
It snows. ("This is a place that gets snow.")
雪が降っています。 (yuki ga futte imasu)
It is snowing. (current condition)
Someone correct me if im wrong but i think ゆきます is very vague because there is no topic marker. The translation would be like "snow, it (something else?) exists" the particle が is used to indicate we are definitely talking about snow as the main topic and ふります means "it falls" so ゆきがふります more literally means "snow falls" or translating to english "it snows" because english likes to verbify nouns.
Someone please correct me if I am wrong, but I believe the main difference is that ゆき means snow when used as a noun. As in ゆきがあります - "There is snow" or ゆきです - "It is snow" so you would need to include a verb like ふる in order to say "snow is falling." I am not sure what the verb is for "to snow" ゆきます, I am less familiar with unfortunately, but I find it in the form of 征きます、meaning "to conquer."