I'm using 3.5.3, and I want my logo to link to www.mydomain.com rather than www.mydomain.com/blog/ which is where wordpress is installed and it links to by default.

Is this possible?

You should be able to just put the URL you want your logo to link to in the WordPress Setting>General>Site address (URL) box.

Be aware if you put the incorrect address in the box above that - WordPress address (URL) - you will not be able to login to to the backend of your site without making changes to the database so be sure of the addresses you put in those boxes.

Sorry it took so long for me to try this, but I finally did, and it caused the entire blog to render without a css file... which was pretty strange.

Any idea why that would be?

My bad... I misunderstood what you were trying to do. Am I correct in assuming that you want to type www.mydomain.com/blog and get to the site. Then if you click on the logo you will go to www.mydomain.com?

Yup, exactly.

Try this, I just did a write up and put it in the FAQ:
How to make the Logo link to another URL

Bingo, thanks!