Looks like wget can do what we need. Speed is not especially important here. According to the documentation, it can even do some posting, which will be needed. Thanks for the tip!
If high performance isn't a requirement, you could install wget or curl and use the system exec function to call it. If you do need performance, you could technically develop a wrapper for libcurl, but it may be more trouble than its worth.
Of course, for some reason I think I read somewhere that the labview functions used curl in some way (in which case why would XP be different?), but that could be totally made up.