I haven't painted a horse and years but a great reference site is called: Rio Rondo. The artist paints very large scale horses and has a great book for sale on her site.
I like the Daniel Smith colors for horses. I believe they are Quinacindrone Orange and Brown.
You can start with a base of Burnt Sienna and just add whatever you like to get the tone the way you want it: Mars Red, Mars Brown, Brown Madder, etc.
For shading, I would add Brown Madder Alizarin and a little Mars Brown or Black to make it a little more opaque. For the deep shadows, you can add Sepia, Indigo or Blue Black to your shadow color.
For highlights, I would use bright colors like Cad. Red or Cad Yellow. They make furs and horse skins more vibrant and "alive."