It's basically just the same as colouring in a colouring book, except you have even more colour choices.(:
The biggest tip that I could probably give is to experiment. Try out all different sorts of colours, and use references!
Bays aren't just brown/red with black points, they often have oranges, yellows, etc. Shined up show horse pics work perfect as refs if you like to use the eyedropper tool and get the colours off an image without having to pick them yourself. Blacks are almost never actually coloured using black :p Make sure you use a lot of blue, green, purple, red tints as shadows/highlights/base colours; they turn out soo much better than using just grey, black and White.
I started out by using free lines I found on dA, as long as the copyright stays on them (with exceptions to some owners rules) you're good to go.(: JNFerrigno has some amazing linearts (the blood bay one I did); if you search her name on google her website should pop up as the first or second link it gives.
Also, I usually change the layer I use to put the colour on to "multiply", as it won't cover lines.
There's also quite a few tutorials out on the internet, they're also really good for giving some steps until you can figure out your own styles.(:
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