What is more correct to say:
One summer's/winter's day.
One summer/winter day.
For example: "One summer('s) day we decided to walk in the park"
Both are equally correct. The day can very much belong to summer, or it can just be a day during summer. In this case it only matters how the author wants to say it. Summer's has a way of sounding a bit more romantic.
The British National Corpus (bnc) has 36 quotes for "summer day", but none for "summer's day", though "summer's day" is in dictionaries. But when "summer" is an element in compound nouns it is mostly summer: summer camp, summer house, summer school, summer time, summer vacation (AmE), summer holiday (BrE). For AmE this may be a bit different, but I don't believe that there is great difference.