Until today I used Twhirl, but I want to give TweetDeck a chance.
However, it seems that I can only either minimize it to the task bar or close it; both options aren't ideal.
Is there an option to minimize TweetDeck to a tray icon?
Plenty of ways to skin this cat if the program doesn't offer the feature 'Minimize to Tray':
TrayIt! will do the trick.
TaskswitcherXP can also minimize any application to the system tray (but as the name implies, only works for XP)
And then there is Pitaschio which can also 'Minimize to Tray'. i'm using it to tray email clients and web browsers.
Of course all these programs are free.