While I'm very privacy conscious, I don't really see the benefit to hiding my region in the DNS request. Because the very next step after the DNS is my browser making a request to their webserver, at which time they will have my actual complete IP anyway.
It's not just the website's DNS server that received your subnet information; it's every single location in the chain of DNS resolvers. That includes TLD servers run by data mining companies. Does Verisign need to know that 2001:2345:6789::abcd is looking for news.ycombinator.com?
With caching in place these methods of data gathering aren't all-encompassing, but if you visit some new or uncommon domains you'll be more likely to become part of the dataset.