For chestnut I usually use light brown with some orange thrown in. It works surprisingly well, given you don't burnish your colors (press really hard). For the dappling, I just use gray-on-gray and layer up! I hardly ever/never use black or white. I use white to blend burnished colors (which I almost never do any more) and rarely use black to accentuate shadows. Otherwise, I rely on mixing/blending colors and their tones.
Dapples are hard, though! It takes some focus to get them done.
I like to use a blue/purple base for chestnuts, and build that up with oranges to get the depth of colour you need.
This is a bit more of an advanced skill though, as working out where to put the blues/purples can be a bit confusing! When I look at a photograph, instead of seeing just the main colour, like orange for a chestnut, brown for a bay etc., I instead see the underlying colours which, combined, will create the obvious colour.
Since I work mainly in pastel, this technique works well. If I tried to draw a chestnut horse just using orange and brown, it would lack the depth I try to achieve in my work.
Dapple greys are tricky, and take practice practice and more practice. I use a pale blue base and occasionally some light purples depending on the horse (or yellows, again depending on the horse) and build up from that.