Is this instrumental case? Why isnt the preposition "W" used here? I havent seen this sentence construction before.
"W zimie" also works.
I'd say that it's not exactly Instrumental, it's an adverb that looks like the Instrumental version of the noun. Just like "wieczorem". And yes, I think I'd be more likely to say "Zimą" than "W zimie" in such a sentence.
The acceptable versions, according to this website (http://ulalupinska.pl/miniporadnia-zima-lato/) are: wiosną/na wiosnę, latem/w lecie, jesienią/na jesieni and zimą/w zimie.
Is there a reason why we would be 'in' summer or winter but 'at' autumn or spring?
I wouldn't think about "na" as "at". In fact for a moment I was really confused, thinking that you're asking about English - why would you? :D
I don't know the reason. The website I linked also says that the author couldn't find any explanation 'why'. It is how it is, I'm afraid...