Would simply dropping some very large concrete blocks on stainless chains as anchors do the trick? It would give you some options for moving things around later.

Otherwise drive some heavy metal pipe into the ground. It will stand up to ice much better than square posts. The corners apparently get ground off of wood posts as loose ice bangs around, but the pipe can take the hit.

Putting in heavy posts would be fine though, can always back-fill the holes with some concrete to provide some stability so they don't as easily tilt later.