it could also be said like that:
''hayır, yağmur yağmıyor, kar yağıyor''
and that would be the exact translation of the 'translated english sentence'' :)
in this sentence, since the two verbs are the same verb that is 'yapmak' you can use değil instead of the negated one. it is same for the below example.
Ahmet gelmiyor, Ali geliyor = Ahmet değil Ali geliyor = Ahmet is not coming Ali is coming