I don't have an iPod to test this but if iPods can be read as mass storage devices then you could use the USB/USB Mass Storage drivers available for MSDOS. Windows 3.1, being based on MSDOS, uses whatever drives MSDOS provides it access to and the iPod would (in theory) show up as a hard drive.
If this isn't possible then you're stuck. iTunes itself will not run on Windows 3.1 because there's no 16-bit version and 32-bit extentions (Win32) will not be enough to force iTunes (or even a new enough version of QuickTime) to think it's on a 32-bit OS. I'm not even sure if iTunes will run correctly on Windows 95 and if that's the case then 3.1 is beyond doubt out of the question.
As for Windows 3.1 on an iPod I can only think of one way to accomplish that - install iPod Linux, compile Bochs for it and install away. Installing's gonna be impossible with no mouse or keyboard so follow the tutorials for Windows on a PSP but alter accordingly to accomodate for the differences introduced by using an iPod. Don't expect it to run at all quickly, that sort of device would have trouble running even Windows 3.1 and I could imagine it would even be sluggish during the DOS parts of the boot sequence.