Unfortunately, the Ontario Milk Marketing Board has decided that cow milk is cow milk and it's bad for business overall to market any of it as different from any other.
In fact, all cow milk is technically sold to the OMMB by farmers and is then resold to processors to package as table milk, cheese, yoghurt etc.
Upper Canada Cheese, which makes two great artisan cheeses at Jordan Station in Niagara, obtained on of the few exceptions to source and label as such its milk from a nearby Guernsey herd.
It wasn't always that way. When I was a kid in southern Ontario in the 1960s, we still had access to "Guernsey Gold" milk, and a Jersey brand as well (delivered to the house, mind you.) Then along came the twin hammers of the OMMB and Becker's low-price corner milk stores.
It's interesting to note that while the quota system has served dairy farmers fairly well in the ensuing 40 years, no one's getting rich from the actual dairy farming these days. You're only guaranteed a profit if you can produce your milk for less than what the OMMB is paying. The price is intended to take into account ongoing input costs etc. but profit is not guaranteed. Until, in most cases, when it comes time to wind up the operation and sell off the quota licence. (You can't sell cow milk legally without quota in Canada. Nothing to stop a person from buying a cow and milking it for themselves and themselves alone.)
Unfortunately, most Ontario dairy farmers milk Holsteins because of the efficiency issues (they produce the most volume) while Jerseys, Guernseys and even Shorthorns produce less milk in a year but it's higher butterfat. Because farmers are paid partly on the composition of the milk some have a few cows of these other breeds in their herd to boost the BF of the overall milk. And then some farmers are just plain contrary and have the an entire herd of Jersey, Shorthorn etc. because they like the breed and always have.
All this is a big reason that most of the innovation you see in dairy products in Ontario comes with sheep and goat milk -- the OMMB does not oversee these products (although dairy farms and processors are all licensed by gov't.)