I've read your comment/question a couple times. It's hard for me to get a feel for the place.
Not sure if the ponds are natural or man-made?
I'm not sure, when you walked the ponds, were you on the bank? Or, walking the water side of the cattails?
Years ago I trapped a "flood control dam", that sounds similar to your spot. That dam is over 40 acres, I trapped around, maybe 1/3 of the shore line.
Wearing hip-boots, I could wade at the outside edge of the cattails. So, you're looking at 2 feet deep, or so? Part of the pond was frozen over, that I could walk on, part of it was just skim ice. I used my ax as a prod. Just to kind of feel around. A shovel would have worked better, but I needed my ax.
Today, if I'd trap the same pond, 40 acres of it, I'd use funnel traps.
Do a search in the archives, should be in the "trap/equipment" section.
That flood control dam was drained and rebuilt, about 20 years ago, there aren't many rats in it today. But I remember nights after school, checking traps, I'd turn the truck around and see 8, 10 maybe a dozen rats sitting on the ice, in the headlights. 40 yards away.