Horses touch each other constantly, and most of it is not the picture people assume they are looking at. A great deal of contact between horses is practical: scratching a place the other one cannot reach, or working out who moves first. This is not that.
What is happening here is contact for its own sake, between two animals that choose each other's company. Horses form preferential bonds within a band, and those pairs are stable: the same two will stand together, doze together, and keep station on each other through a whole day of grazing. Muzzle to muzzle, breath to breath, is how they greet and reassure.
The sequence ran like this: one grazing, the other moving up alongside, a moment of contact, then both heads back down. No dominance in it, nothing resolved, nothing gained. Two horses that like each other, briefly saying so, and then going back to the grass.
On printing this one: the picture is built on a shape, the arc two necks make when they meet. That reads instantly at any size, which makes it the most forgiving of these images for a small print and the obvious one to give as a gift. It also hangs well beside one of the single portraits.