At present, the mounts of World 3 are all the same, with a little difference that some can fly and those who can fly are generally bought. You have no choice but to go to the store to buy a horse yourself. It's all sent randomly by the system. All horses have the same attributes, the difference is your bonus points. There are many kinds of horses. For details, you can go to official website to check or ask experts and senior players in abilities. What kind of horse do you ride? Just changing the shape of your horse has no effect on anything else.
The spirit beast will increase the movement speed and increase your attribute points according to a certain proportion. This has nothing to do with the spirit beast, what school you are, but the level and growth of the spirit beast. World 3 has many growth routes, so you need to ask yourself whether you want to add some horses to various sects. I am YL, unlike you, so you still have to go to official website and ask in the game.