Writing Windows desktop applications on Linux?

How can I make a programme that runs on Windows, but is developed on Linux?

I have an idea for a side project. It's a programme that would make certain kinds of images. It's something I could do on a website, and in fact I will be launching a web version. However I think it might also work, and might work better as a desktop application.

Most of my market is going to be mundane home users, everyone's sterotypical mother. Windows is the most popular OS here. I also don't want to complicate things by requiring software that the average user can't easily install.

However I run Ubuntu, and that ain't changing any time soon. So how can I develop it on Linux and have it run on windows without the user having to install a lot of stuff?

Java? What about native widgets? Is there anything I can do with Mono or .net? Or is this pretty impossible?