A possible way to approach backgrounds would be to first determine what you wanting to draw the most attention to in your painting. For instance lets assume your horses face is the “focal area”. There are a couple of different ways you could approach this.
Some artists use dark against light to highlight an area so you could darken the background against his light face and lighten it around the dark mane causing high contrast - but also lighten it around his hindquarters which will reduce contrast and not draw attention. I’ve seen a lot of portraits where the background is darker around the hair (assuming the sitter has dark hair) which softens those edges and reduces attention. That would be one approach. (Sunny kind of did that on her bird painting. Had she used the abstract background around the entire painting the bird would be lost. But the light against the hard edge of the dark wing attracts attention and the light against the head gives it a glow. Pretty nice. )
Another way would be to give a “glow” around your subjects main focal area (face?). Described in David Leffels book as having the light burst so powerfully onto a subject that it caused the color to radiate into the atmosphere around it. Done by bleeding the subjects color into the background directly around the focal area kind of a foggy haze of color.
But as to your question of what color to use, I had an artist tell me to mix up all the colors on my palette that I used in the painting and use that. Hmmm. Maybe. If you did that you would likely get a cool grey and a very cold painting. If you went with a brown black as you mentioned, consider dulling it or de-saturating and warming it to give it depth and softening the color so the hindquarters have less contrast than the face.
Hope that helps or at least gives you some food for thought? :)