If we ever get the ability to make more buttons in popups. Instead of just YES/NO I could fix that by simply giving you several options. At the moment it feels like anything I do to fix one awkward situation will just create another awkward situation

I might look into making a separate hitched wagon status. If you have both wagon and horse and you switch to foot: it could leave the wagon and horse coupled. Where anything you clicked on would count as clicking on the wagon.
That will take quite a bit of extra coding though.