.NET 2.0 is the main requirement. It is present on most Windows machines at this point. For example, newer versions of Windows already have it and older versions often have it because some other program that the user installed, put it there.
You can also look into making an installer that triggers the installation of .NET if not present.
Or you can look into the commercial .NET linkers.
In either case, searching through Google will give you the answers like "installer .net", ".net linker" and variations thereof. This is basically the same issue as for anyone writing code in VB.NET and C#. With the community being fairly large, there are tips and solutions out there.
Regarding Cobra specifics, there is the Cobra standard library which is fairly small as most library classes are coming from .NET. The file is called Cobra.Lang.dll and you would put it next to your .exe, or you can just tell Cobra to embed it:
cobra -c -embed-run-time:yes Foo.cobra
Finally, you mentioned Wine. While you could try that approach, Cobra runs well with Mono which runs on both Linux and Mac. Mono comes with a linker/packager out of the box, although I have not played with it much.