Okay, it's clear from the glossary that you can wear the boots on the broom (although you can't use the movement bonus), and cannot use the cart. So, what about the horse? It seems like you should treat the horse the same as the boots... but that's a pretty hard thing to picture.
I'm tempted to say no, even if the rules imply yes. Or would that punish the poor dwarf further?
I'm not sure what you found in the glossary. In the Movement Points section, it says "Thus a hero with boots (but not with cart or horse) can ride on the magic broom ...." I can't find any other entry that mentions both the cart and the broom.
The BBC series is far better than the excellent NBC one. Now go watch it.
This is not me but I have been known to dance like David Brent on occasion.
I would play this that the horse/cart is left behind if you decide to use the broom. It doesn't make sense that those can be carried along and hoarding all the movement bonus itmes is just not cricket.