A lot of native C++ code will actually just compile and run on C++/CLI. This is really a kind of hybrid compiler that can call native Win32 functions and use standard C libraries like OpenGL. You can even call COM interfaces directly (all the stuff you can do with a native C++ compiler).
The .Net library is also available but for these you create managed classes (using the ref class keyword). You will use gcnew to allocate memory for these classes (from a garbage collected heap). Memory for your normal classes is still allocated using new and delete (from a standard, non garbage-collected heap).
In short, you can migrate to .Net in bits and pieces, though there is still some friction when switching between managed and unmanaged classes.
I found this book useful: Pro Visual C++/CLI.