Is there some sort of GNU/Linux software that would allow me to do a network inventory of all the software installed on our windows_xp machines and then update the installed version (of Mozilla) to the more current version?
First of all this isn't a Linux question and secondly it isn't a (Linux -) security question, so: moved.
Interrogating machines, getting an inventory for about anything, is easy done using Ms-specific WBEM adaptation called WMI.
You could script a scheduled task that'll trigger an inventory on a list of machines when an update comes out, then parse the output.
That was the easy part. I don't think there's generic OSS SW for rolling out updates/installing SW on w32.