I am not that much up on trees. I think where SF lives there near the SD Badlandsthe Rocky Mountain Juniper ( think they are sometimes called Silver Cedar) is probaly the native cedar.
Wher I live the Red Cedar or Virginia Juniper is one of the prefered conifers for windbreaks. Farther East where you are, they become invaders in pastures so are not favored. The Virginia Juniper produces seed every year, that is the female trees do. The Rocky Mountain Juniper takes two years for the seed to develop. They might not be as troublesome. Are your tall trees cottonwoods? If you are in an area where they get plenty of moisture leave them, they like their feet in water, in the right places they will live for years. If you have dieing Elms, you might as well take them out. I still give the old Siberian or Chinese elm some credt, for if it had not been for that tree, people here may have never attempted to plant trees, but they only live about 25 years.
Dead trees and fallen trees still offer some benefit to wildlife, so you have to take time and evaluate what you have and what you want in the end.