Is grass greener in areas where cow graze?

Yes, if the pasture is managed properly so that the grasses get significant rest after being grazed. The feces and urine from the cattle that have grazed there add fertilizer to the soil that the grasses grow, and the grazing action also encourage vigorous foliage growth in well-managed pastures.

However, the grass is not greener in areas where the cows have just been pulled off of (i.e., the very day the cows are switched to a new pasture), or if the pasture has been severely overgrazed due to poor pasture management.