There are several ways to go about this that could be made to work, depending upon your exact goals. The simplest way is probably just to create a Visual Studio "makefile" project that fires off a custom build command to run a makefile you've built. But that keeps you away from a lot of the nice benefits of Visual Studio as an IDE, so I'm guessing that's not really what you're after.
If you want a more fully integrated solution, you're going to need to do two things. First of all, you're going to need to change out all of your include/library paths to avoid the Microsoft ones and go after the Cygwin ones instead. You can do this by selecting "Tools->Options" from the menu, then choosing "Projects and Solutions->VC++ Directories" from the tree on the left hand side of the window that comes up. You'll have options to change the search directories for executables, headers, libraries, etc. For what you're trying to do, I'd suggest removing everything and adding in just the cygwin directories.
Second, you'll have to tell Visual Studio to use the gcc/g++ compiler. This is a bit trickier. VS supports custom build rules for custom file types... but it seems to have C++ hardwired in for the Microsoft compiler. I don't really know a great way around that except to use your own custom file extension. You can try the standard unix extensions of .c (C files) and .cc (C++ files), but I suspect Visual Studio will automatically pick up on those. You may have to go with something totally foreign.
If you right click on your project in the Solution Explorer and select "Custom Build Rules" you'll be given an interface that will let you create your custom build rules for the file extension you've chosen. The interface is relatively straightforward from there.
This might not get you exactly what you wanted, but it's probably about as close as you're going to get with Visual Studio.
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