Is it possible to mine Bitcoins at a pool through the TOR network? If so, how would one configure the appropriate tools?
You could mine over TOR, but I would expect you would get much higher stales & downtime due to the high latencies of the TOR network.
You can use the application ProxyChains to force any application on your computer to use a proxy (or a combination of proxies), simply add a new proxy to ProxyChains, 127.0.0.1 as IP and your TOR software's port as port, and then setup Proxychains to force your mining application to use that proxy.
I've written an application to accomplish this on my own time. Hoping this helps you and anyone else who comes across this answer.
The test results that I've used over tor and the stratum protocol, I seem to have an average latency of 610ms to a Monero Pool such as
pool.usxmrpool.com. This may vary for other cryptocurrencies, but using Tor there is no stales in 4 hours of testing.