@zerowinger66  
Those are all very good choices.

@mjangelvortex  
One candidate might be the Huma Bird or Simurgh of Persian mythology. They seem to have fantastic/magical elements to them, and appear to have similar aspects to the Unicorns in mythology (impossible to catch, symbols of good omen). And while they might be portrayed more often as being similar to the Phoenix in writing, the griffon-like statues in Persepolis, Iran are thought by the locals to represent the Homa Bird  
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An alternative candidate might be the Egyptian Axex. It’s associated with royalty (much like Unicorns are with royalty/aristocracy in FiM), and the noted three protrusions on their heads could be seen as a crest, or maybe even horns (like Unicorn horns), and those could be adapted in universe as being a similar conduit for magic.

@zerowinger66  
They could be now that you mention it. They could be like the “Earth Pony” of the Griffon types. But what type of Griffon would be the “Unicorn” type?

Wingless? Cool. Alce or Keythong Griffons would make a great addition to the MLP mythos.