Get dimensions of logo

You can use getimagesize() for this purpose:

list($width, $height) = getimagesize(esc_url( get_theme_mod( 'mitch_logo' ) ));

echo ".logo {
    width:{$width}px;
    height:{$height}px;
    background: ...;
}";

If that adds a little milliseconds to your page load time, I can edit this to provide a JavaScript version of the answer 🙂

Hope that helps.