Conditional Menu based on Season

Looking for a solution. Park has two different seasons - summer and winter. Want to show different menus based on the season.

Idea is to have a “Summer” and “Winter” button in the header.

Different menu shows based on what the user selects, but we can set the default depending on the time of year. In the summer, we default to the summer menu...

But we have shared pages that will remain the same no matter what the season. Home, contact us, directions, hours.

The original idea was to actually build two different sites domain.com/summer/ and domain.com/winter but then you can not share posts, Events, and other pages. Too much duplication. So we think that may be a mistake.

Any ideas come to mind?