I'll throw another color option in, black chestnut, although I agree this horse is most likely a brown.
Also, the coat could be darker depending on turn out. Horses turned out only at night during summer months do not get sunbleached.
I owned a mare that was registered chestnut, had to do a color change after she had three bay foals by three different chestnut stallions.
She was actually black if I only turned her out at night.
Brown. The unofficial "official" way to tell is the brown hairs on her muzzle.
Ah - but not always! In my other thread I questioned if my black mutang may be brown because now in the winter he was showing brown hairs on his muzzle. And most felt he was black because while there was some brown on the muzzle and lighter brown on his tail his other soft tissue areas really were not lightened. So looks like I have one of each.
Now I do have another question. We know how the smutty/sooty gene can even make palominos look really dark. I wonder what it would do to a brown with it? And have they decided mealy does not work on black-based horses? I know they used to say what is now brown were blacks with mealy.