On two separate occasions, after exploring 4000 meters from home base on horses I had found along the way, I dismounted, created a nether portal, and ignited it. The tamed horses cannot travel through the portal, whether I use a lead or if I push them through. They simply will not go to the nether.

I have two horses (separate locations) far from my main base that refuse to travel through nether portals that I had planned to use to return to base. However, other horses can enter the same portals. The issue seems to be specific to the horses themselves, rather than the portals.

I brought the one of the offending horses all the way to my home base and found that it will not go through any nether portals, no mater where they are in the overworld. I have tried portal shapes in the following X:Y dimensions: 2:3, 3:3, and 4:4. Other horses can travel through the portals as normal.