Using the following command (/setblock ~ ~2 ~ minecraft:end_gateway 0 replace {ExactTeleport:1,ExitPortal:{X:571,Y:67,Z:602}}) I attempted to travel trough an Exit Portal, while on a Horse, back to my house.

According to my F3 bug feed, I arrived at my destination as per the co-ordinates, but all I could see was void. I could not move or dismount the Horse. Reloading the chunks also had no effect. I only escaped the void by entering the same /setblock command again with the same co-ordinates, which fortunately reloaded me where I intended to be, but left me with a saddle and leather (the Horse didn't make it). I've found that you can pull a mob through on a lead or push them through the portal, but it seems to glitch out if you are physically on the mob. I have not recreated the environment for fear of getting stuck!