I looked for Wine in Debian Wheezy and found it's not in the repository. Apparently no one volunteered to maintain the package. Hunting down dependencies and compiling it for myself seemed like far too much trouble, so I had a look in Squeeze.
The version of Wine in Squeeze is old (1.0.1) and my game wouldn't run in it.
While looking into the absence of Wine in Wheezy and the age of the package in Squeeze, I came across PlayOnLinux which is an application designed to make playing Windows games with Wine on Linux easy. It installs its own more up-to-date version of Wine.
The version in the Debian repository is old and only uses Wine 1.3. My game wouldn't run in it. I decided to try installing the latest version, and was pleased to find there's a Debian repository.
The latest version of PlayOnLinux installs Wine 1.5, in which my game seems to run pretty smoothly
PlayOnLinux includes scripts for installing a variety of games and applications, including Microsoft Office and Internet Explorer 6.
I've installed Steam and want to try out Half Life. I tried it in Ubuntu years ago and Half Life ran less well on my current laptop with a 256MB video card than it did on my old laptop with a 16MB video card. It will be interesting to see how it runs under the latest version of Wine.
However, as my old laptop could certainly have run the Dora the Explorer game with too much trouble, and my current laptop only just copes, I think I may need a much more powerful machine to run Half Life in Wine as well as this machine did in Windows.
Note on using Wine in Debian: I was stumped at first as to how to install a Windows program in wine. The GUI way to do it is to launch winefile in a Terminal. I think Ubuntu had this as an option in the Gnome menu, and it's easy to put it there in Debian from Main Menu.