Do you have to leave the geese to go to bed on their own, or are you there to herd them in? We bought a pair of geese and quickly trained them to go in at night. We used a mix of putting their corn and fresh water in their shed (6x8 garden shed with added pophole) then herding them in using two long canes as Dans does, or brightly coloured fly swatters in the form of hands - different but it worked. They would happily stay out at night if we didn't put them to bed.
Once they flatly refused to go into the shed but I think there was something in there. Another time I heard them in the night making a huge kerfuffle in their house, but by the time I got there all was quiet. We found that we have a weasel so guess it was that and that it would have left pretty promptly on being confronted with, now, four big hissing geese. When the nine goslings were around, fully grown, they all fitted into the same shed comfortably.
I think a pig ark would be fine, if you can make it fox proof and still be well ventilated - geese like to go to bed wet, so need ventilation overnight. They also like plenty of clean straw, especially when they are nest building - their nests are wonderful.
Our geese free range but we find that they don't range far, no further than the hens. Our property is surrounded by tall hedges which discourage them from flying, although they do take off sometimes, but they don't explore the full extent of their possible range.