Horses will not always go through Nether portals. I was able to take a horse through 2 nether portals, then on my way back, it didn't go through the next one. I've tried leading it through, getting on it then getting off once inside portal, everything. I have had this occur twice now, and the first time after a few days, the horse could go through the portals again.

There are no blocks in the way of the horse or anything. The horse just doesn't want to go through.

To try recreating this, maybe take a horse through a couple different portals a few times.