One Site. One Theme. Multiple Stylesheets without plugins?

One simple solution that might meet your needs would be to add the published year of the current post or page to your body using body_class(), and then add the appropriate styles for each year to your stylesheet.

Here I add a new css class to the html <body> element like “.year-2016” using get_the_date() to fill in the year. Note that you should always use body_class() in your body tag:

<body <?php body_class( 'year-' . get_the_date('Y') ); ?>>

I suspect this will be too simple and broad a stroke, and you will want to conditionally add this css class to your body only if it is a page or a single post the user is viewing, for example. Otherwise just load the body tag normally:

<?php if( is_page() || ( is_post() && is_single() ) ) { ?>
         <body <?php body_class( 'year-' . get_the_date('Y') ); ?>>
    <?php } else { ?>
        <body <?php body_class(); ?> >
<?php } ?>

Then in your main stylesheet you could style any menu’s and other elements for posts and pages published in 2016. For example your main menu could have a different background color:

.year-2016 .main-menu {
    background: #0cf;
}

This method would be very dynamic, and requires little additional coding to implement the new CSS for your different year themes.