Well, I can only speak for Dexters, not really "miniatures." It seems as if a lot of people are crossing everything with everything to get something smaller and I, personally, wonder where and how that will all end up.... many of them are using Dexters to accomplish the "small" part...Dexters are an old (rare) breed, the smallest true "breed" of cattle, intended as a family milk cow for those who need a gallon or two of milk a day, not 5 gal., and a beef carcass that doesn't require your local Safeway freezer to store it. The meat is supposed to be great and I will find out in a couple of months when we "86" a steer. I guess some people DO keep them as pets and lawn ornaments...hey, why not? They are naturally horned, can be black, dun, or red. We raise breeding stock and some are quite small (we have a couple of 37" cows); others are larger (42" or so). Excellent mothers! Obligated to say that, as with any rare breed, you have to show care in selective breeding to avoid the proverbial "gene pool with no lifeguard!"
Yes, as Dun says, there's a "miniature cattle group," and there is also a Dexter group: http://groups.yahoo.com/group/dextercattle2/