Keep in mind goats need anywhere from 3-6% of their body weight in long fiber. Unless your goats are babies and assuming your bale is 80-100 lbs I would think a 4x2 bale would be used well before 3 months.
The bales out here are usually about 100-110 lbs. Seldom less than 100. I have never seen smaller bales for sale either. But 3 months seems like a very long time.
Mine are only 8 months old rite now. we have had them for a Lil over 3 months. so 1st bale lasted about 3 months. I know as they get older it will go quicker.
Now what if I put up a sheet of plywood in the front. would leave a 2' open space on right side to walk in. then I can move the top places of wood on the sides and back down a few inches to add more open air flow. would that work
Well, you can do whatever you feel like trying. If you completely enclosed it with only an opening on one side, will you still have room to maneuver bales in and out? Everyone's situation is kinda unique and you'll try a few things/mods before you find what works for you (typically).
Until you get the logistics worked out as far as what would work for you on a day to day basis, wouldn't a $10 tarp to throw over it at night and take off in the morning just be the cheapest easiest thing to do? That way you can try some different things as far as where you would want the door, how wide it would be to make getting in and out with a bale, and other things like that. Otherwise I would close in the room completely with a full plywood door so that the 4 foot wide opening would make getting in and out easy. Leave an air space around the top of say 4 inches on a couple of sides then you can leave the door open on days that it is nice to get good airflow to help to keep it dry.
Tarp ON or ABOVE the hay? When I got the small bales this summer from the farmer up the road for the alpacas I got a month ago, he said it was best to NOT have a tarp right on the hay since that can keep moisture in and it can mold. If I did need to protect it from roof leaks (really old barn) tying a tarp above the hay so air could still move around it is better. Fortunately there are no leaks over where the hay is stored so I haven't had to deal with that.