Good questions. Would you have the ability to manually remove snow from the top of the ice? If so, the maximum depth of the pond becomes less of an issue. Light penetration is key in order to keep phytoplankton and rooted vegetation from dying and consuming oxygen during prolonged winter ice-overs.
My feelings are that if ten feet is adequate in Nebraska with 2' of ice, then 12 feet should be adequate up north with 4' of ice--provided that light is allowed to penetrate. Any chance of using aeration of some type to keep the ice from completely covering the pond? If so, I think you could configure your system to allow for good water quality throughout the winter.