Hi I know this sounds quite not practical but still I would like to ask: How possible it is to compile a program, originally written in Objective-C for iPhone, to an application that runs on windows mobile?
What I will be doing is to implement the app with C# again. But before that I want to know if there is such cross-compilers that can save some work.
There are no cross-compilers that will do this. You have to rewrite the app.
Your only hope is to compile a win32 dll that you can link to from C#. I think the closest you are going to come is Cocotron but that doesn't do what you want either right now.
You can compile C or C++ code for Windows Mobile 6.X and earlier. With that said, you could re-use the business logic of your iPhone application assuming it was written in C or C++. You would need to write a Windows Mobile GUI using WTL or MFC. You won't be able to make use of the Objective-C or Objective-C++ code on Windows Mobile.
I agree with ian1971, that you may write an app in C# on the platform, MONO, which may help you a little big.
You could write the original iPhone app with MonoTouch, then it should be fairly trivial to port it to Windows Mobile (.net compact framework).