I’m a newbie here, but I know a bit about cows. Feedlot cows are fed corn (as well as antibiotics and hormones). Free range cows forage on whatever is available. So the taste of fresh free range milk changes constantly depending on what the cows are eatting. It is probably really difficult to get consistant flavor with fresh free range milk, but as far as I’m concerned I won’t use store bought milk.
I wouldn’t assume that the burned up grass is giving unusable milk. Hay after all is just dried up grass. Calves have to nurse regardless of the weather and they do fine. Taste the fresh milk. If it tastes good, it will probably make good cheese.