Move disk to new hardware? I've got an OS X Snow Leopard Server config on a Mac Pro 1,1.  I can't upgrade any further on that hardware.

However, I've got a spare MacPro 3,1 and wondered if it would be "simple" to just move the disks to the new hardware?

I thought I'd ask first just in case the disks get updated with something which means I can't go back to the old MacPro.
Checking the specs of the the MacPro1,1 you should be able to upgrade to 10.7.5 if you upgraded it to at least 2 GB of RAM and you don't need Rosetta (for PPC-apps).

Since the preinstalled system on the MacPro 3,1 was 10.5.1 and both are equipped with a SATA (3 Gb/s) internal HD-interface, there shouldn't be any problem to move the "old" disks.

Your disks won't be updated with anything, except you initiate it yourself.