The bug

Horses do not make wood sounds when walking on Nether wood, bamboo wood, cherry wood, or stems.

To reproduce

Put a horse on a platform made of different types of wood. Push it around and observe that only the Overworld wood types will produce the intended sounds. Use the attached resource pack to help.

Solution

Also check for bamboo_wood, nether_wood, cherry_wood, and stem sound types when checking for the wood sound type.