Archimedes can give you an aging point if you answer his question correctly
xanthos can give a hop randomly

The only divine horses that you can interact with for prizes without needing to be the owner of them are;

Frost. You can defrost one a day, for a chance to win a Hypnos' Blanket. It's a decently high chance, too, and happens pretty often.

Archimedes. You can answer their horse trivia questions each day. The first Archimedes you correctly answer in a day will give you an ageing point.

Topaz. You can congratulate 5 of them each day. You'll 50 Equus per Topaz, or you have a tiny, tiny, tiny, infinitesimally small chance of getting some passes instead.

Xanthos. You can stroke 5 Xanthí each day. The first Xanthos you stroke in a day will give your most recently born horse +10% energy. After the daily update, each Xanthos gives a Horn of Plenty to one randomly selected player from among those that stroked that particular Xanthos the previous day. If you pick 5 good Xanthí that aren't being stroked by many other players, then you can get several Horns of Plenty each week this way.