Yes she is def. a chestnut, some call this black chestnut. In Arabs and QHs you see the red m/t a lot more and in Morgans you see a more straw or greyish colored mane as much as the red mane. Either way that's a cool color and not a bad looking horse. Too bad my bronc busting days are OVER...
Here is a younger one at an earlier stage (and kind of sweaty)
https://www.blm.gov/adoptahorse/horse.php?horse_id=3309
They also had a couple silver bays on there.
Every mighty oak was once an acorn that stood its ground.