Then I struggled with the colour and had to do a huge colour chart to work out where I was going wrong.
Answer: don't use Cad Red Deep or Med as it appears to have a base of blue notes. Thus the glorious chestnut you are aiming for persists in developing a sickly, greenish hue.
I used Transparent Oxide Red and Cad Yellow Medium. To darken it I used Viridian. To darken it a lot I also added Dioxazine Purple. Despite appearances there is no tube brown. I find tube brown (Burnt Umber) a risky colour to put anywhere near yellow or orange. Those blue undertones again.
Photographing the finished painting was a pig because the camera wanted to turn the entire horse the same shade of luminous orange as the sunset. Still, turned out nice in the end, as my Mum used to say.
The original reference photo of the mare is by AinslieG. Thank you Ainslie!