For the special mounts youll need to tackle some tough challenges on ultimate warrior difficulty, which unlocks after beating the game once. Start with shadow runner by preventing that stone barrage during escape from wan castle, might be tricky but worth it. Red hare needs you to take down lu bu in battle of xiapi without any healing items, while storm runner opens up when you keep 7 allies alive in huarong path on the wei route. For hex mark, focus on protecting 6 officers during chibi while playing shu's story.

The regular horses are actually a bit easier to get, just need to work on those peace levels in different areas. Build up ji province to level 1 for birch, push liang to level 2 for chestnut, and get you and jing provinces both to level 1 for maple and mahogany, respectively. Something interesting about those special mounts - they start right at level 30 with maxed stats, while regular horses need some time in battle to level up.

Tip: might be smart to focus on the regular mounts first while you're getting comfortable with the gameplay, then tackle those special mount challenges once you've got more experience under your belt.