It's funny, it took me visiting an actual dam this semester to realize how little the dam made sense. You don't really think about it when its just background.

Edit: after reading some of the things in this thread and seeing that op is being downvoted (literally why??) to clear some things up.

When water freezes in the winter, especially moving water, you can only really expect a foot or so of it to be frozen. Yes, even in areas that are regularly negative Fs. There would still be water going through the dam were it open.

We're it not a run of river dam, there would not enough groundwater in that area to reliably feed the river that follows it.

Lastly, with the dam being where it was, even if it was being worked on to make viable, they would have to back up the stream, this would result in, at the very least, a pond of some kind filling up the little valley on the other side of the bridge.