Greyhounds are a sight hound and I would suggest probably not very good as a deer dog as this is a domain ruled by scent hounds, and yes the natural instinct to chase pretty much anything that runs would be just about impossible to overcome.
They do however use them to cross over more stocky breeds for pig dogs and for "coursing" (not sure on terminology) deer in countries where it's not illegal. (Coursing is what I had explained to me by a Scottish lad where they use dogs to chase down deer in the open much like a pig dog would)
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