If ever my goats are ill, the first question the vet asks is .....do they run with sheep? I personally do not keep my sheep with the goats but people do mix them.
My own personal view is that goats need feed all year round - obviously the pygmy goats do not need much. But, most of the feeds contain vitamins and minerals which are important, and at least here, I do not think they would do well without hard feed. They are fed hay all year round as well, and never leave any.
With the pygmy goats its not so much getting over, as getting under the fence, and even through the bit of gate between the gatepost and the gate!! Being small, and agile, they can get through the tiniest space. I use sheep netting, as close to the ground as possible. They do not seem to respect electric fences, and get tangled in it.
Some of mine are in pig arks, with half doors, and others in field shelters, with a gate across, which is closed at night. We are high up, in an exposed area, and they have managed fine in some bad winters.