It sounds totally natural. There's nothing wrong with grammar in the sentence, but I've never heard someone say this sentence. Due to 도 of 올 수도, which means "also, too, or either", this sentence may be said in a very limited context. And this context is not likely to be given in real life but maybe in literature works, I guess.
The question is somewhat misleading.
Although OP seems to be asking the difference between "수" vs "리", but the existence of "-도" in one sentence but not in another might confuse people.
The correct comparison should be "눈이 올 리가 없어요" vs "눈이 올 수가 없어요" unless i'm mistaken.
Both "수" or "리" is used to describe possible outcome based on existing premise.
Latter is more generally used to describe when the premise and conclusion have direct logical relationship...like weather.
For example, if it's sunny and summer, there is no way it's going to snow.
Hence "오늘 같이 해가 쨍쨍한 여름 날에 눈이 올 리가 없어요".
So it is generally used to describe most reasonable/logical outcome.
However sometimes you wish to describe some possible outcome not necessarily in a direct logical manner.
It's more or less logical, but there are missing links to describe the deduction process.
For example, when kids are grow up, they are bound to get hurt.
Maybe because they are careless, likes to run around, etc, but whatever the direct reason is it can just happens.
(When describing unavoidable outcome, this expression often conveys a minor nuance of resignation)
"애들이 크다 보면 다칠 수도 있지 뭐"