A .DAT file is probably not a program. Linux files don't need an extensions, like .exe to run. Likewise many linux files don't even use extensions, (extension being the three letter code after the dot, (.dat .exe. doc)
It could be that the .DAT file is a data file for another program. Maybe that other program is for linux. Can you tell me more about the file, where it came from and what you want to do with it?
If it does indeed need a linux program to run, you probably can't use Cgywin immediately. Most linux applications have source code available. Programs for cgywin are compiled a certain way so as to work in Windows. You could see if there is a pre-complied bianary for cgywin and get that or you could get the source code, a compiler, the development files and headers, the needed libraries and compile it yourself. (No this is not a simple option, cgywin is a very nerdy tool).
Best options if you do indeed need linux in Windows are:
1. Use a Virtual Machine. A virtual machine can run another operating system as a "guest" in side another. You can install Sun's version for example, (there are other versions,) and then use it to run your favorite linux distributions right inside windows. Ubuntu, Kubuntu, OpenSuse, Fedora, Centos, LinuxMint, Puppylinux, or any that can run on the cpu will work this way.
https://www.virtualbox.org
Alternatively, you can install Linux side by side with Windows, so that when your computer stats you choose which Operation System to start. This isn't what you asked for in your question, but I am throwing it out there. You could also use Wubi:
"Wubi is an officially supported installer for Windows users that allows Ubuntu to be installed and uninstalled in a safe, easy way as with any other Windows application."
https://wiki.ubuntu.com/WubiGuide