Possible in zone 4? Maybe. I have a friend that was working on a project to try to breed some trees with cold tolerance genetics. He did find one or two mature persimmons in the north. He said they were growing on folks lawns in town. My guess is that those trees were somehow protected from the cold by the original owners when they were young. His theory was that in areas where there are no persimmons that they would be deer magnets.
My personal view is that zone pushing for wildlife trees is usually not worth the effort. Many backyard orchardists love to zone push. They worry about micro climates and protect trees when necessary. I think they just enjoy doing it. Lots of nurseries are pretty liberal with zone ratings and those zone rating often vary from nursery to nursery for the same tree.
I think we are better off first finding trees that are well suited for our areas. In order to attract deer, there needs to be enough food. A single apple tree in an area that doesn't have many apple trees won't do much in my opinion. Deer either need to have that same food available in the general area or they need a concentration of it. A dozen apple trees together might produce enough apples to be an attraction. Similarly, a single apple tree that is secluded in an area where deer are used to eating apples may also do the trick. If you are zone pushing, with persimmons, your trees will likely be the only persimmon trees in the area. That means you'll at least need one male tree or a "perfect" tree. Persimmons are very slow to fruit. If you have to take special measures to protect them from the cold, it will be a lot of work and they may die anyway. Compare that to a tree that is well suited for your zone that requires little if any care.
I'm a big persimmon advocate. They are my best bang for the buck tree, but they grow natively here.
Thanks,
Jack