Cows tend to graze downwind. When they are cudding they will face whichever way they feel like (and cows lying down DOESN"T mean it is going to rain!) which will usually be into wind if it is more than about 15 knots. If you land near them they will come and stand in a big circle around you, have a good look and a satisfying scratch against any pointy bits on the aeroplane, then go off and do whatever they were doing before you landed. They will stand in a solid line across the runway when you want to take off and will usually get out of the way just in time.
Very true about a field with only one "cow" in it!!
Sheep will usually graze into wind. They are very very very stupid.