I read this thread at Minecraftforum.net

https://www.minecraftforum.net/forums/minecraft-java-edition/survival-mode/2963160-horses-in-the-nether

and decided to test it.

I built a Nether portal (in Creative mode), spawned in a horse and pushed it into the portal, it just stood there without porting.

I tested with a bunch of other mobs including several horses, all of the others ported normally.

I used /data get entity >UUID< to check the Portalcooldown:, when it was standing in the portal the cooldown was at 300, when it was outside the portal it counted down to 0.