I don't think there is a limit to how far they can travel under the ice. How far they are likely to travel is another matter.
There is often large air pockets under the ice, especially if the water has dropped.
Some times a partially submerged log will have air trapped under some part of it, and a beaver may have several burrows into the bank all around it's pond.
I would think the more important question is why would a beaver want to use that channel after freeze-up.
Just a guess but I'd think that they spend 90 percent of their time close to the lodge and feed bed. The larger beaver will check out the dam regularly but I've seen no evidence of them going further then that. With one exception.
During breading season, January and February, the breeding couple will often leave the main house and spend a week or two alone in a love shack somewhere else on the pond.
The love shack may be nothing more then a bank burrow or it could be a old abandoned lodge.
I have seen where they will travel several hundred yards under the ice to reach such a love nest.
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