I guess this question would exist of two sub-questions. I'm currently unable to test this myself so i figured someone else probably already has or is willing to try this. I was wondering since mobs can teleport through the nether-portal (since a few updates back) if it was possible to get your horse to follow you to this place of horror and disaster. And if the answer to that question is "yes" then i would also like to know if horses are affected by any slowing effects. In this example in particular i meant soul-sand but i guess this would also count as potions etc.
Yes, you can transport horses through the nether. I've successfully transported horses from one base to another via paths through the nether, avoiding oceans, so I know they can go through the gate. It's a little tricky getting them through; for whatever reason, I found that when handling several horses, they would avoid going through the direction I was pushing them but easily wander back out of the nether on their own. Pretty sure that's a quirk of randomness, but you'll want to have leads and fenceposts handy so you can immediately confine them far enough away from the portal that they don't walk back out.
I play in multiplayer primarily, so I found it handy to have one person behind the horses pushing and one person in the nether grabbing them with leads. The leads will break when you and your horse are in opposite dimensions, so it's not exactly trivial to go through. They will not go through while being ridden, so you have to make do with pushing and pulling.
I ran a test just now; horses are definitely affected by soul-sand. Splash potions of slowness are a lot less effective: I could hardly tell a difference in horse speed, but the particle effect indicated the horse was being affected by the potion. They also have trouble with one-block-wide tunnels and even two-block-wide tunnels sometimes, particularly around corners, so it's recommended you carve a three-wide, three- or four-tall path for riding in the nether.