I think in the movie they did it to make Spirit stand out more :]
From an artistic perspective it's also much simpler and easier

What Rin said basically, but also making Spirit stand out much more as a unique character I imagine. ^^

Troll and Blaze have the idea, realistically.

The model would most likely be a mix of Granite and other background horses, copy and pasted / recycled. The ones of alternate shading/coloring are all hand drawn and animated like Spirit and some of the other horses.

The basic answer; they're all basically NPC's like in video games.
NOTE: If you look at NPC's in certain games they're all rather cruddy and 90% of them actually look alike, recycled models and all.

they could be baced off Comanche a chestnut horse who survived the battle of little bighorn the battle the man the colonel is rumored to be baced on died

Bay and chestnut horses are the cheapest and the most popular so probably majority of real cavalry horses were brown.