A certain amount of it is conditioning. If a goat is used to alfalfa, of course he won't want to eat grass hay! Like a person used to eating steak and baked potatoes having to eat chitlins and cornbread (yummy)! But a goat will eat most anything if he has no other choice. Here we overwinter our meat goat herd on leftover hay from our hay selling business. Any hay that is too wet, gets rained on, stalky, etc gets saved for the goats and cows and the good stuff gets sold. We feed no concentrates whatever and ours seem to do OK on the mixed grass hay. Now that is for a meat goat herd on "low management" not a dairy or a high managed meat business, which obviously would need more for milk output.
My 2c, once they get used to the poorer hay, they'll eat it as well as the other. If you notice weight loss or poor body condition, give a little grain, and make sure they are worm-free going into the winter. Another thing, I know with cows they can lose up to 30% of their body mass over winter without detriment, as they put it back on with spring grass. This is probably true with goats as well, though the thought of allowing a goat to lose weight over winter is a big no-no to most goat people. Yet it has been proven that overwintered cows can lose 30% of bodyweight and still rebound in spring to where they were before winter, and are in as good health as those that were kept fat all winter. I'm not an apologist for starving animals, just that I think most people go overboard in giving more than the animals really need, after all...just how did those goats survive for thousands of years before alfalfa and 12% grain pellets?!