If it's in .NET core, does this mean that WinForms will become cross platform (without having to use Mono)?

Looks line no, unfortunately

> To be clear, the Windows Desktop component is only supported and included on Windows.

https://docs.microsoft.com/en-us/dotnet/core/whats-new/dotne...

If only Microsoft cared to listen feedback a bit... the lack of a cross-platform UI (which existed for a while with Silverlight) is what is dragging back the whole .net ecosystem from wider adoption.

Unfortunately no, though I believe there are other attempts at cross platform GUIs whose names I can't remember at the moment...

Uno [1] and Avalonia [2]?

[1]: https://platform.uno/

[2]: https://github.com/AvaloniaUI/Avalonia