To be clear, Objective-C refers to Cocoa, since C # refers to .NET, or even when the Java language refers to the Java platform - this is the main way to do things. Objective-C can be used wherever the compiler supports it, but Cocoa frameworks are indeed the most valuable part of the equation.
It should also be noted that (os OS X) Safari is a Cocoa application, but iTunes is not yet in use (it still uses the obsolete Carbon APIs), so I'm not sure how it works on Windows. Apple has ported some important parts of Cocoa to the Windows DLL for loading Safari, but as far as I know, this code is not available for public consumption. (One can imagine that Apple really does not want to simplify the creation of reliable applications for a competing OS, they published only two key applications to achieve their goals, such as the adoption of iPod / iTunes and the core browser WebKit.) Do not expect these Cococa-Windows libraries to become widely available; if they do, it will come as a surprise to many of us.
As already mentioned by @Gregory, GNUStep and Cocotron are plausible options to explore, but I suggest thinking long and hard about whether you really should do what you ask. By and large, Microsoft tools have much better support for Windows, you will encounter fewer undocumented restrictions, and their native applications will "feel good" for Windows users. I found out a while ago that although I like Objective-C / Cocoa, if I ever had to write a program for Windows, I would do it with the C # / platform. NET