Anyplace the ice is over 1/4” thick, beavers will typically not go under that ice. Otters will, muskrats will (close to shore) but beavers will not.
I once had a county job where a homeowner who lived near the dam was watching it for me. The ditch connecting two lakes was open water, but the lakes had ice. One day they called me and said “there is beaver messing around the dam, can you come get it?” It was about a 20 minute drive and by the time I arrived the guy had shot the beaver. Now this guy had an old single shot .22 he had not shot in years, and it had absolutely no sights, just a bare barrel.
The story he told was informative. He shot over a dozen times at the beaver from a distance of less than 15 yards. The beaver would start to swim up the ditch toward the lake that was about a half mile away, but he would run ahead and chase it back toward the lake at his end of the ditch where the dam was, which was right at the lake inlet beside his house. The beaver would swim right up to the edge of the ice, him popping off shots at it anytime it was on the surface, but it would not go under that ice. He finally managed to figure out a crude sighting system and was able to dispatch the beaver. He said it would swim back and forth at the edge of the ice, diving when he would shoot, and pop back up and repeat.
That is how averse beavers are to swimming under ice - although of course they do it just far enough to get a branch from the feed pile in front of the winter den, but that’s it.
As a boy first trapping beavers, I had no real instruction. I would continue to run body grips in beaver runs after ice-up. After a couple years I noticed I had never caught a beaver away from the den under ice. I still caught the occasional muskrat and even a few mink in 330’s under ice, so all was not for naught.
