For what it's worth, I had some trees on my dam, before recent renovations. Black walnut on the backside, and some smaller willows on the front, along the waters edge. My dam is a thick old cuss, so I was in good shape. They were removed, with no bad results. The willows, on the waters edge, My guy said that usually with black willows, the roots grow parallel to the waters edge, and don't do any DEEP damage. They want the water and follow it. From the photos, I cannot confirm what type of trees you have though. Your dam looks pretty thick to me. My Black Walnut trees were getting close to 12" diameter, and the willows were nothing like you have. They were much smaller.
