OS is not independent of hardware. If you want to virtualise a 64-bit Operating System - or for that matter, if you want to use any of the latest virtualisation products - you need a 64-bit CPU as such products are no longer 32-bit compatible.
You'd also want to ensure that the CPU has support for Intel-VT or AMD-V technologies. Typical 'Hypervisors' like Hyper-V need this technology to perform the hardware-assisted virtualisation using the CPU.
-Matt