The "desktop app packs" for WPF and WinForms Microsoft has made very clear that they will not support anything other than Windows. (They also won't directly be a part of .NET Core according to diagrams, but packages installed on top of it.) It's also unclear if they can be open sourced (they probably cannot be), and if they can't be open sourced it is unlikely a community-led effort could easily work on making them cross-platform.
WinForms work quite nice on Linux with Mono. Won't they cooperate?
That said, this may still be a great opportunity for .NET Core to encourage trying Mono in its documentation for enterprises looking for cross-platform support. (Hopefully they already knew about Mono by this point, but an extra push won't hurt.