The One Cow Project

I would like to raise one cow, or more correctly a steer, for beef.  I am interested is buying as little feed as possible and keeping this animal on My 10 acres.  I have read about rotational grazing and am wondering how many acres of pasture would be required for one head.  Since I live in S.E. Michigan, is there an any chance of winter grazing?  I have read about a bread called Dexter came from the Scottish Highlands and it may be able to graze outside in my climate all winter.  If I could leave enough tall grass standing in the fall I may not have to buy much feed through the winter.  At this point I am just in the thinking and research stage, maybe in a year or two I can act on it.