Geese have an average body temperature of at least 104F, a thick down coat, and a unique circulatory system designed to provide excellent blood flow to extremities. They are more comfortable in cold weather than in warm weather.
Safety from predators is a completely different issue.
Nuthen, depending on the breed of geese, they can do quite well in small yards, too. For instance, my dewlap toulouse, who are on the lazy side, do quite well in small yards. You could get away with a yard as small as 50' x 50' for a few geese, but it requires more maintenance than a pasture.
nuthen, 80% of a goose's diet should be grass/weeds, with a couple of cups daily of grain/complete feed supplement. They graze all day long, just like horses. If you have good pasture, an acre can support up to 30 geese.