How do you play a bare horse versus horse endgame?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws for movement, checkmate and both repetition rulings: a side that forces a repetition by perpetual check or perpetual chase loses rather than drawing. The chase half has not been validated against the official casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it before publishing.
Direct answer
With nothing else on the board, horse versus horse is generally a draw with accurate play from both sides. Neither horse has enough independent force to overpower the other or to force a breakthrough against careful, central defence, so the practical goal for both players is usually just not blundering the piece away.
Why neither side can normally force progress
A single horse can defend itself and its general's immediate surroundings adequately as long as it stays reasonably central and does not wander into a position where it can be trapped or forked by the opposing horse. Without additional material to create a second threat, there is rarely a way to overload the defence.
Where the practical danger actually lies
Games are not lost through some forced technique here so much as through a horse getting stranded on the rim of the board, blocked by its own leg at an inconvenient moment, or wandering within reach of a fork. Keep the horse active and central, and treat any drawing chances your opponent creates with the same care you would in a more materially complex position.
Related questions
Does having soldiers on the board change this a lot?
Yes, considerably; the addition of even one soldier each can turn a clean draw into a genuine fight, which is covered separately at horse endgames.
Is this endgame ever worth playing on for practical chances?
Against a weaker opponent it can be, since the drawing technique, while simple, is not always intuitive to a less experienced player.