Seen a couple pictures of dairies recently. Always interested in them. Here's a tweet, leading to a Post article on the Canadian dairy flap, but the article doesn't have the tweet's photo.
IMHO the cows shown are dirty. Since it's a conventional setup and the focus of the article is Wisconsin dairy, and it's only April, my guess is that the cows mostly stay in the barn, as our cows did, and that's why they are dirty. But our cows would get dirty because they lay down, got their tails in the gutter with the manure, and spread the manure to their flanks and legs. In the setup shown, the cows are raised up on a platform, so the manure can spread across the lower driveway behind them. (Likely have a skid-steer small tractor to doze the manure.)
Do I have a point? Not really. Given the realities, cows are going to get dirty part of the time. Perhaps for the big dairies where they never get to the pasture they're going to be dirty all the time.