I doubt that this will work.
windows mobile is not windows, there is a different kernel, it's built on the windows CE kernel not the full thing.
the drivers for the printer that work on windows xp are not going to work on windows mobile 2003.
Any exe file won't work unless it's been compiled specifically for windows mobile.
whilst you may be able to take open source programs, and use a copy of visual studio 2003 (not free) to compile for windows mobile 2003, (with the windows mobile 2003 SDK (free if I recall correctly). it's not exactly an easy job.
After this you'll still have to figure out how to connect the USB printer to the PDA, (i'm not sure if your PDA has a USB port, most PDS's don't (given that they don't have the available power to be able to have a properly spec'd port available.
It's easy to make a raspberry pi the host machine because it's already got a proper USB port, it runs Linux where there are already drivers available, the software is easily ported to the Raspberry Pi system, and it can either be run headless, or just plug into a TV or whatever. the Raspberry pi IS a computer.
whilst the PDA is a computer too, it's different architecture, different operating system etc will probably cause problems.