I'm using 64bit Windows 7 but it should shouldn't make a difference, leave a comment if you run into difficulties and I'll help you out.
Anyway, I did a little digging to make that behavior stop. If you use an alternative browser follow these steps to make sure Tweetdeck uses it, too.
Very simply, go to Start and press "Default Programs". In the dialog box that opens up:
When that opens you'll see the following dialog box:
Press the two little arrows on the right of "Custom" to expand it. The first option should be for your browser:
Makes sure all those "Enables..." are checked off and choose your default browser.
Press OK all the way out until all are closed.
Tweetdeck should then use Firefox as your default browser.