As a rule of thumb for your larger trees close to the dam (please read "rule of thumb") a tree's root system rarely exceeds the span of it's branches. Keep in mind that a BOW may encourage the roots to deviate from this concept. I would think about removing any undesired trees above the 4" diameter that are on the back side of the dam especially if the branches are not over hanging the top of the dam. This rule of thumb should help you determine if the roots are protruding through the dam far enough to eventually rot away causing the tunnel for water leaks. I'm sorry I can not be more exact, but hopefully you can make some judgment calls on what trees to cull.

If you have any Osage orange hedge, locus trees, or catalpas, you should use Tordon RTU to kill the root system or you will have a ba-gillion little trees growing up from the stump or surrounding root systems. It is easy to use and does not cost much although it's warning labels would be worth reading, seems like pretty nasty stuff.

Dropped trees in the pond make nice structure/habitat. I left a few overhanging trees when my pond was renovated that will eventually fall into the pond as the bank has washed away and I don't even like walking under them, they are that sketchy. Eventually they will add to the pond environment. Be warned that dropping too many green oaks (I believe, maybe others as well) into a pond can potentially cause a fish kill due to the tannins that leak out of the tree into the water. Maybe someone can chime in on how many would be too many.

If you take out a lot of trees and leave them lying, you will be allowing more light to hit the ground causing more growth of who knows what. This would cause maintaining the dam to become a real pain with all the tree trunks and limbs lying around. Just imagine trying to weed eat a bunch of brush with all the hidden trip hazards lying at your feet. I would at least cut it up, throw it down hill and make some rabbit shelters (piles) at the base of the backside of the dam.

Fish on!,
Noel