There are several ways.
First you can install a filing system driver as @redbeam_ has indicated. This gives (more or less) native access to the files. Though extreme care should be taken due to the many differences between Windows and Unix-like filing and operating systems.
Alternatively, you could install a virtual machine application such as VirtualBox, install Linux into a VM and attach the partition to the guest OS.
However, since this question was originally asked in the Raspberry Pi forum, there might be another way for you which would be to leave the partition in an active Pi and simply access remotely using WinSCP. With this, you can directly edit files on the remote Pi from Windows - this is what I do when developing on the Pi.