Geese would be happier free ranging all the time but if that's not possible, spending some time in a pen won't hurt them. The more room they have in the run, the less stressed they will be. If you do decide to raise them in a pen, try to make sure they get a few hours of free ranging every week.
I've had full grown American Buff Geese killed by great horned owls twice. Since a raccoon can reach forty pounds I am certain that they could kill one if they wanted to. I've also lost geese to fishers. But stray dogs are probably the worst.
I lost some of my Pilgrims to an owl last year. I know it was an owl since I can't think of anything else it could be. Some of the younger adults that could still fly managed to somehow jump through a window we had open in their pen one evening and were killed in their pasture. The only noticable damage were a few puncture marks on the base of the neck.
When I plucked the feathers off I found that the entire area around the shoulders, back, and lower neck, was a giant black bruise. The owl didn't eat the birds - I don't think it was able to carry one off and didn't want to eat it there.
Before this we had been letting a big old Embden gander loose with a few hens and for the entire year he was in the backyard we never lost him or his hens. That made us a little more relaxed than we should have been about the pen design.
Opossums probably aren't an issue. Foxes definitely are, as are coyotes and stray dogs, as have been mentioned. I'm not so sure about raccoons. Considering how smart and determined those little demons are I'm sure they could figure out a way to do it. But they'd have to survive getting whomped by the goose's wing-spurs.