A panting cow may be a sign that not all is well within. Whilst I was at Greg Judy's mob grazing school, nutritionist Mark Bader explained the role of nitrogen in the diet, and how an excess of it, in the form of urea, reacts with the haemoglobin in the blood and reduces the blood's oxygen carrying capacity.
He says cows breathing hard is often a sign of too much protein in the diet, something they get from grazing pastures when they are all leaf and hence high in protein, rather than a combination of leaf and stalk, when the carbohydrate:protein ratio starts to become more balanced. The cows pant harder and harder in an attempt to get enough oxygen to their muscles.
A quick google search corroborated the effect of urea on the blood, so there could be something in this. Also, I spent some time watching the cows today. They're grazing quite mature pasture, and even though the late June sun was blazing down, none of them were breathing hard or looked in the slightest bit distressed.
Except for the recently introduced bull, of course...