Update:

Turns out I did win something but it was at a time when I wasn't on my account? Do you just stroke Xanthos during the day then later on you get your reward?

Thanks

You can stroke up to 5 different Xanthos each day and during the game update in the morning, there's a chance that each Xanthos who got at least stroked once by a player the day before give a Horn as Plenty and 1000 equus as reward. The player chosen is completely random between all players who had actually stroked that specific divine.

Means if you're extremely lucky you can win up to 5 Horn of Plenty from 5 different Xanthos each day.
The less players stroke the Xanthos, the higher the chance you can win something due to a smaller field of competitors within this "raffle".
So best is to stroke a Xanthos from inactive players or pick some from the directory by yourself and not from a popular link list on player's profiles as these tend to be frequented regularly.

Lovely, thank you. That info was super comprehensive.

Thanks again Eleyii