Can a horse look purple (ish)?

I think this is mainly an artefact of image processing, combined with the light in the photo.

This could be accidental or deliberate. A crude automatic white balance process could get confused by all the green and shift the colours away from it (i.e. towards purple), especially if the image is also being lightened. The post was old, so in-camera white balance is likely to have been crude. Alternatively the original picture could have been adjusted to match the photographer's perception.

Here I've divided the image into 3 stripes:

• The left is untouched.
• In the middle I've pushed the white balance further towards green using GIMP's auto white balance tool, exaggerating the purple.
• On the right I've tried to recover it by reducing the gamma of the red and blue curves, i.e. darkening these components. Increasing the brightness of the green channel and then darkening the whole image has a similar effect. The resulting greens in the background are noticeably brighter, but not unreasonably so. I've probably slightly overcorrected in demonstrating the effect.

The lack of shadows and near-white sky where it shows through (blue pixel values reach 100%, red and green don't quite) suggest an overcast day, which enhances blues.

But note that roan horses with black hairs are known as blue roans, suggesting that they can look bluish in some lights