Can I package up a .Net web application (that normally runs on Windows 7 etc) to run in a Docker container, and then execute it on ‘any’ host supporting Docker? 
Such as Dockers on Linux or Dockers on Windows etc? 

One Solution collect form web for “Can I run a .Net web application on Dockers for windows?” 

You can at least use dotnet core image. 

From Getting Started with .NET and Docker:

.NET Core is the open-source version of .NET which is available now.  It has a different focus from the full .NET and it’s a modular framework, so you only include the parts you need – the framework itself is composed from NuGet packages. 

Before you can run .NET Core apps on a Linux (or OS/X, or Windows) machine, you need to install the DNX runtime.  This isn’t the full .NET runtime that we have on Windows; it’s a slimmed-down .NET Execution Environment (DNX). 

When you define a Docker image, you start from an existing base image, and the sixeyed/coreclr-base image which is publically available on the Hub already has the DNX installed and configured.  To containerize your own .NET Core app, just use that base image and add in your own code.