With the current .NET Core you can not run Winforms applications, it is possible however to mix .NET Core and .NET Winforms projects in one solution, I would recommend using .NET Standard
as the common code base used by both .NET Core and Winforms.
If you have patience you can wait for the new .NET Core 3
, for now only the preview is available: How to port desktop applications to .NET Core 3.0 | .NET Blog
Also see: Bring WPF and WinForms Apps to .NET Core 3 with Telerik UI