Can you partition hard drive on Mac mini so I can run windows.

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Of course. You can install Windows on a virtual machine or Boot Camp. To know which one is better for your uses > https://discussions.apple.com/docs/DOC-3321

If you decide to use a virtual machine, you don't need to partition the Mac, as a virtual machine uses a virtual hard drive. You can use Parallels, VMware Fusion or VirtualBox to create the virtual machine, and you can install the Windows version you want. Try VirtualBox first, as it's free and enough for most users.

If you decide to use Boot Camp, Boot Camp Assistant (in /Applications/Utilities) will guide you through the steps to download the Windows support software and partition your hard drive. Note that your Mac only supports some Windows versions officially > http://support.apple.com/kb/HT5634 You have to buy a full or System Builder version at Amazon or NewEgg.

Then, follow the Apple's steps > http://manuals.info.apple.com/en_US/boot_camp_install-setup_10.8.pdf

If you mean running Windows under Bootcamp the answer is yes and you will find more information here. If you mean running Windows under a thrid party emulator such as Parallels Desktop or VM Fusion it is not necessary to partition your HD as they can create a virtual disk drive for the windows installation. The advantage of the virtualization approach used by Parallels and VM Fusion is the ability to run Window applications on your OS X desktop complete with the ability to copy and paste from OS X to WIndows and back.