If a skeleton trap horse wanders into the Nether, triggering it will give an 80% chance of wither skeletons as usual for spawns in the Nether. But triggering a skeleton trap horse that has wandered into an ice biome will always spawn normal skeletons, not strays.

On the other hand, if the world has an appropriate biome at the origin and (0,0,0) is open to the sky (i.e. someone broke the bedrock all the way down to the void with Creative or cheats), triggering a skeleton trap anywhere in the Overworld will have an 80% chance of strays as the riders.

The cause is that the creation of the skeletons for the riders sets the new skeleton's position after calling the "onInitialSpawn" method, so the check for whether it should spawn as a stray uses the default position (0,0,0).