I tried to research your question, but could find no information - credible or otherwise - which would suggest a deliberate behavior. So, my answer is just a guess.
First off, Canada geese feed by dipping their head under water to feed on vegetation. As others said, this action can create enough surface movement as to prevent the water from freezing. But my observations of local Canada geese say otherwise: we're experiencing temps in the single-digits over the last several weeks, and the geese are happily playing (?) on the ice of a normally slow-moving river. So wherever they're getting their food from is anyone's guess - but it's definitely not from underneath the water.
If you're seeing the geese in cold weather, then you're seeing the urban-adaptive nonmigrating Canada geese, and, that means, they've found ways to adapt by eating and nesting in ways that are different than their migratory brethren.
So, to answer your question, I would say "they could - but only for more warmer cold climates, and not at all for very cold climates". To suggest "they would" suggests an instinctive action on their part, and I haven't seen any information to support this.
You mentioned it is a local park pond. If the pond is artificially fed via a pipe below, that could be the reason that the water moves above and does not freeze over. It could also be that the pond feeds the pipe for local use. In this case, artificially moving the water using bubble machines could be in use (like that used on the sides of boats that are moored in fresh water to prevent freezing along side it).
One last thought on why there would be a hole in the ice (which I realize is not what you asked) is, maybe there is runoff from local streets? This would add salt to the water, if your area does salting in the winter. This could create a salinity in the water that is both agreeable to the Canada goose, as well as make that part of the water less able to freeze. When that saline water is diluted as it mixes with the fresher water away from that entry point, that water can freeze.
Living with Wildlife - Canada Geese
Somewhat unrelated to your question, I found that the name of the bird is actually "Canada goose" (branta canadensis), and use of "Canadian goose" suggests its citizenship! LOL The link here gives examples and counter examples of other species' names, and shows why language (especially English), in my opinion, is a stupid form of communication...
Canada (or Canadian?) geese