The bug
This affects horses, donkeys, mules, magma cubes, slimes, shulkers, and sniffers.
Once horses/slimes/magma cubes/shulkers are in minecarts, it is very difficult to free them, as their hit box is much larger than the minecart. You just end up hitting the horse/slime/magma cube/shulker instead of hitting the minecart.
You can free them by breaking minecart from underneath by making a hole.
How to reproduce
/summon minecart ~ ~ ~ {Passengers:[{id:"horse"}]}
/summon minecart ~ ~ ~ {Passengers:[{id:"shulker"}]}
/summon minecart ~ ~ ~ {Passengers:[{id:"slime",Size:1}]}
/summon minecart ~ ~ ~ {Passengers:[{id:"magma_cube",Size:1}]}
/summon minecart ~ ~ ~ {Passengers:[{id:"sniffer"}]}
Linked issues
is duplicated by
relates to
Attachments
Comments
Reopened because of the hitbox bug.

Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
It has been patched, although horses still fall into the world if you break the mine cart their in.
No, it definitely still exists.
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 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.
I did the above slightly differently, while the horse is in the ground, mount it and then jump 🙂
Sadly i lost a good horse to this bug... i tried to free him by sending the minecart into a lake Should have read this first...sigh..
..

Is this still a concern in the current Minecraft version 1.7.4 / Launcher version 1.3.8 or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
I can confirm that the bug still exists.
Confirmed for 14w11b, but now activator rails can get off horses automatically.

Confirmed for 14w21b
Like Gary Closse said, now activator rails can help, but still a problem
*Added screenshot
confirmed for 14w32b

Confirmed for
1.8.4 however fixing this "bug" is probably nearly impossible because the hitbox of the hourse is simply bigger than the hitbox of the minecart
Not really Marcono1234, it just involves some relatively simple changes to the way Minecarts work.

Affects Shulkers in Minecarts as well in 16w15b
/summon MinecartRideable ~ ~ ~ {Passengers:[{id:"Shulker",Health:0.1f}]}
Confirmed for 1.13 & 18w30b.
Please keep the ticket updated.
Confirmed for 18w31a.
Confirmed for 18w32a.
Confirmed for 18w33a.
Confirmed for 1.13.1.
BTW: Also happens with Slimes.

Confirmed in 1.15.2 and 20w22a.
Confirmed in 1.16 Pre-release 2.
Confirmed in 1.16-pre3.

Can confirm for 1.16.1 and 20w29a
Can confirm in 20w51a. I'd just like to add on that this affects slimes and magma cubes with a size greater than or equal to 1. Here are the commands I used to reproduce this issue.
/summon minecart ~ ~ ~ {Passengers:[{id:"horse"}]}
/summon minecart ~ ~ ~ {Passengers:[{id:"shulker"}]}
/summon minecart ~ ~ ~ {Passengers:[{id:"slime",Size:1}]}
/summon minecart ~ ~ ~ {Passengers:[{id:"magma_cube",Size:1}]}
Can confirm in 21w03a.
Can confirm in 21w05b.
Can confirm in 21w06a.
Can confirm in 21w07a. Video attached.
Can confirm in 21w11a.
Can confirm in 21w14a.
Can confirm in 21w15a.
Can confirm in 21w17a.
Can confirm in 21w19a
Affects 1.17
Can confirm in 1.17.1.
Can confirm in 1.18.2 and 22w18a.
You can run them over an activator rail to dump them out of the cart. I'm not sure there's any way to fix this, except by making their hitboxes arbitrarily smaller.Â
Can confirm in 1.19.
Can confirm in 1.19.2.
This also affects sniffers since they're now able to enter minecarts. I've updated this ticket accordingly.

Can confirm in 23w16a & 1.19.4.
This isn't duplicate. This report is about the buggy Horse's hitbox, not the mobs falling into ground.