When searching on Google from a browser, the actual search query is visible in the address bar of the browser, even when using Google's secure search (https). Is there a way to submit the search query via POST instead of GET, so the query terms aren't visible in plain sight in the URL? This is to prevent snooping by network administrators.
There is no use to this. As you know, HTTPS prevents your network administrators (or anyone else in between you and Google's servers for that matter) to see the request (so the URL but also the POST data), unless the admins have monitoring software on your computer or make you use a proxy. If they do, they can also see what you are sending via POST. So I don't see a scenario where POST requests might be useful if you use HTTPS and simply delete your browsing history (you can set the browser to do that automatically when you close it).
It might be a little less obvious in logs or tools when you use POST requests, software might be meant for displaying URLs, but technically there is no difference. If you still want to use POST for some reason, I think you're going to have to use a proxy service for Google.
DuckDuckGo, a search engine focused on providing more privacy than Google, has the option to use POST requests instead. On duckduckgo.com/settings, go to the privacy tab, and there you can set whether the address bar shows your query. DDG has more advantages though, you should give them a try if you are concerned with privacy. There are also some tools for developers, like automatically searching popular programming language's documentation (e.g. /?q=strpos).
But then again, if your pc is bugged, they can see POST requests if they want to. If it's not, then HTTPS suffices.
And I also wouldn't recommend doing things you shouldn't do on other people's network. Sooner or later it'll be found out, and might get you in trouble.