Unlike Java edition, ridden entities can still not go through portals, eg. a horse or a minecart.

Steps to reproduce:

1. Ride a horse/a minecart
2. If you are using a minecart, connect a railway to the portal in the overworld, and away from it in the nether.
3. Go through the portal

Expected Result:

Entity will go through the portal, and instantly.

Observed Result: 

Until you dismount, neither the ridden entity, nor the player (you) will go through the portal.