It is very obviously not running generally towards it under those circumstances.
The line of the hillside that the horse is following heads away to the right of the photo then curves around the top of the manger. Once past the viewer it will be running WSW along the crest behind the viewer. And that's the direction where the sun is, behind the viewer.
It wouldn't even be running NE if it was turned upside down, because it is not on a NE/SW line, as has been pointed out many times now.
From what I can gather, you are saying that if the horse stopped being on a broadly N/S line and was put on a NE/SW line, then it could be argued that it would be galloping toward the sunset. That would make some sense. But the reality is that it isn't 'pointing' SW, it's pointing almost S, where, as George has said, the sun does not rise or set. Never mind the curve of the hill or possible paths it might take, thats meaningless, the thing is not 'galloping' toward sunset!