Yes, it does happen that it snows in October, and some in November. But when that happens, it usually doesn't last, and that is not the norm.
I'd say you want to be here by Oct 1st. But that's only because Fall here is beautiful and you would be here for the foliage that many travel from all over to see.
But if avoiding snow during a move is the concern, most years you would be ok at least through Thanksgiving.
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