OTL of a sort...
I mean the Amerindians traveled from West to East. Filling up the entire continent. But taking this another way. What if the horse survives in the central valley of California but no where else. Then the Californians pull a kind of Ghengis Khan on the entire North American continent? Going West to East.
I think one problem is that moving West to East, colonists run into much more formidable initial barriers at the outset.
From East to West you've got the Appalachians and then relatively easy country until you cross the Mississippi and then get into the harsher terrain of the West. West to East, well, outside the Pacific Northwest and Northern California things start to get arid and inhospitable pretty quickly. Then you have to cross the Rockies.