With Subversion, I used the Visual SVN server to get it up and serving in a few minutes. Is there an equivalent for Mercurial, so I can run hg.mydomain.com?
Mercurial comes with a build in web interface: http://hgbook.red-bean.com/read/collaborating-with-other-people.html
Check out the Mercurial wiki on Publish Repositories here. It contains good information about a variety of different ways to make your repo information available across your LAN or the internet. As Pete's comment said, Mercurial has a built-in, quick webserver for working with one or two colleagues on a temporary basis, but that doesn't sound like it would work for your request.
As an aside, I tend to just use BitBucket.org to host my repositories (public and private) and some bug tracking. You may want to look into their plans and weight that against running your own server. The paid plans allow you to set up CNAMES to point to hg.yourdomain.com to the BitBucket servers.
The PublishingRepositories wiki page gives a great overview of all the different ways you can exchange changesets with people. They range from simple shared files space, to ssh, to the build in hg serve
, to the hgweb/hgwebdir cgi scripts that came with your mercurial installation. You need to pick the best mechanism for you, but the hg.yourdomain.com mechanism you describe most closely aligns with the hgwebdir in Apache solution which is fully detailed on the wiki.
for Mercurial server on Windows, you can get a very good tutorial here: http://www.jeremyskinner.co.uk/mercurial-on-iis7/ or here: http://blog.schuager.com/2010/03/how-to-setup-mercurial-server-on.html
It's pretty easy to set up and works like a charm.