I trapped rats in the ice in Alaska but we didn't trap the lodges. Best locations are "push ups". Look for little bulges in the ice. The rats ball up vegetation and push it up to make air chambers underneath the ice. They use these air chambers to breath while they're swimming under water and they'll also sit in there and chew on root bulbs. It's pretty simple to pop the top of the push up off with a hatchet. Set a #1 or #1.5 trap in there, run a wire out to the surface and wrap it around something to anchor the trap. Put the cap back on the push up and splash a little water and snow around the seam. It'll refreeze and keep the push up from freezing over on the inside. It's a pretty effective way to catch rats under the ice.
Check your regs, also. Some states don't allow tampering with lodges. Probably the best way for you to trap the lodge is to look for air bubbles under the ice. This usually indicates a route into the lodge. You can chop a hole along that route and drop in a conibear. It's usually more work than trapping the push-ups though.
