I would understand "a nyáron" as "ezen a nyáron", "this summer", not the summer in general.

With both the -on and the -ban endings? That would be like "in at Christmas", I think.

Hungarians say "on summer" (literally translated), just like in English we say "at Christmas" -- not "in Christmas" or nyárban.

Not everything is "in" :) (Why is it "in the evening" but "at night" and "during the day"??)