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The skills of the Greek Heroes and Greek Gods are always very high, but it differs every day which one is the highest.
They won't get lower, but they might increase a little bit over time, like a lot of divine horses' skills do.

On the Special Horses page (under Achievements) you can find the Greek Gods, click that and find Hera. Her page says:
""Hera has extraordinary skills that are randomly recalculated upon awakening.""

If you own Hera, you can also find this info in the tab with the 'sun' on her private page (or on the page of someone else's Hera, in the same tab).