Image2Docker may be the simplest path for getting your older .NET apps working on newer OSes. It works by extracting either an entire VM or specific ‘artificats’ from a VM.
An artifact can be a WebForms App running on .NET 2.0 on Windows 2003. This use case has been tested by the Image2Docker user community.
Steps to Dockerizing older .NET apps
The IIS module (artifact) in Image2Docker uses the ArtifactParam flag to specify a single IIS website to extract into a Dockerfile.
This allows the extraction of a workload (IIS/ASP.NET webapp) from a VM into a Docker Image (.vhd):
ConvertTo-Dockerfile -ImagePath C:\whereever\win-2016-iis.vhd -Artifact IIS -ArtifactParam aspnet-webforms -Verbose -OutputPath c:\whereever\aspnet-webforms