I, too, built a half-acre pond, next to the house. Any tree at or above the waterline, we left. A small post oak died the first year. In the third year, a larger post oak died. It's about a 10 inch diameter tree. We left it. Over the next two years, most of the limbs fell off and now we have a "snag", as wildlife biologist Dan VanSchaik calls it. We actually love that solitary dead tree. Woodpeckers have feasted on it, birds land on it. I've seen vultures on it, Osprey several times...all kinds of predatory birds will land on it. I've seen a variety of hawks and kites as they migrate. Belted King Fishers spend quite a bit of time on it. Blue birds have tried to nest in the woodpecker holes, but I don't know how successful they've been. Bottom line...that dead tree is a pretty busy place.
If water infiltrates very far into a tree's dripline, that tree will be affected. It may not kill it, but it will be affected. If heavy equipment damage the roots, that tree will be affected. But, I'm opposed to removing trees using any kind of guesswork. Here's the catch. If the trees live, which many of them will, you win. If one or two die, you still win...you've got new wildlife habitat. If a tree (or trees) die that are problematic (unsafe), then you have to remove them. It ain't an easy task to cut down a dead tree in water.
Trees that will be submerged will die. I'd remove those. But, any that sit at or above the waterline, leave them be.
Figure out where your waterline will be, flag the entire periphery of the pond and then figure out what to do with the trees.
In my opinion, a pond with trees removed above the waterline doesn't look natural, unless it's a lawn next to a house.
