Microsoft has made the Windows Server Core base image available on Docker Hub, and that's a version of Windows Server 2016 which has much of the functionality of the full server edition but without the UI. As base images go, it's very large - 5 GB compressed on Docker Hub, compared to 380 MB for Nano Server, and 2 MB for the tiny Alpine Linux image. But it means you can Dockerize pretty much any existing Windows app, and that's a great way to start migrating your systems to Docker.
Remember NerdDinner? It was an open source ASP.NET MVC showcase app, originally written by Scott Hanselman and Scott Guthrie - among others at Microsoft. You can still get the code at CodePlex, but there hasn't been a change committed since 2013, so it's an ideal candidate for proving that old ASP.NET apps can be migrated...