I had the same problem. What I did to fix this is mount the horses like you normally would (you and the horse are in the cart at the same time) look directly at the cart from above, and RIGHT click the mine cart and you will get off the cart with both you and your horse without either having damage.
Hope this helps!
I went to minecraftwiki and checked it out about an hour ago. Thanks for the info!
I meant left click to destroy the cart. Then dismount your horse and if you walk in the cart riding the horse you will be in the mine cart once again.