I have a hay feeder for my goats that gets filled twice in the afternoon. The amount of hay you should give depends on the goat and the type of hay. I feed timothy from TSC. Throughout the day, the hay runs out and the next day around noon I refill it. I try to keep hay in their feeder on rainy days when they cannot forage. I should feed my goats more hay than I do probably, but hay gets expensive. During the morning hours when they are without hay, they browse around their pasture. My goats also get Dumor grain in the evening, around 1 1/2 for two goats I think. The grain is the last thing I give them for the day usually. I am trying to get them off of grain. I have just purchased minerals for my goats I will be adding to their diet soon. Definitely do your own research, however. I'm just a beginner as well and am always changing my goat's diet.
You are correct that goats are foragers, unlike sheep. If you cut down on the amount of grain, they should get an increase of hay, not grass. When eating plants that are near to the ground, like grass, the chances of your goats getting worms increases. During dry spells, grass can become concentrated with toxins that are bad for your goats, and during really wet spells, grass might not have the nutrients necessary for the goats.
Again, I'm just a beginner trying to help a beginner. Feel free to fact-check me, anyone! Hope this helps!