My American Buff geese manage to make it through windy -- and I mean really windy -- Iowa winters when the actual temperature last year dropped to 20-below BEFORE the wind chill. There's a reason goose down is used for bedding; it's a pretty good insulator.
Mine do not have pool access in the winter, but I keep a large heated dog water dish in their enclosure. Although it really is too small for bathing, sometimes Gussie and Golly stand in it to preen. That honestly worries me a bit, because I couple of years ago, I read about a woman whose wet geese literally froze their feathers to the ground. Even if it was just an "urban legend," I'd hate to take the chance.
To keep my goats' and sheep's water unfrozen in the winter, I use auto water drinker de-icers from the feed store that cost about $40. I've never tried them for the poultry.
Goosebaby offered excellent advice, but clearly has pickier geese than mine. Gussie and Golly will eat ANYTHING if they think the ducks or chickens might want some.