We have Walnut and Pecan trees in our yard. They aren't much better than a cottonwood about self pruning during storms. Our yard has looked like a disaster zone in storms past, but the main trunk of the tree still stands and resumes growing. Deeper roots I guess.And that is why I won't have a cottonwood, or any other soft-wood tree such as sycamore, near my house.
Glad everyone is okay, but talk to the insurance company about taking that tree out.