winforms is not web. Web is Web.
Web means HTML + something (usually JavaScript, CSS and probably jQuery or such).
1 - If you need a web application, and want to do it with .Net, create an ASP.Net Application.
2 - If you need a Windows application (Desktop), create a WPF application.
3 - If you need a Windows 8 "Metro" style application (a.k.a Windows Store App), create a WinRT XAML application.
4 - winforms is completely useless. Forget that.
If your customers don't want to install any version of the .Net Framework, your only option is #1.
A winforms application will NEVER be a web application, regardless of any hacks you do to make it run inside a web browser.
an XBAP (WPF Browser Application) is also NOT a web application. It's just a regular WPF client application that does not have it's own window.
Edit:
If you did things the right way (that is, maintaing separation of concerns and putting application logic in Controllers or ViewModels instead of the horrible code behind practices most winforms developers are generally used to), It should not be that hard to reuse your application logic and create a new application (web or otherwise) while maintaining the Data Access and Business Logic layers intact.