Thanks to the Internet, finding a list of famous people who have birthdays in January was easy. I wanted to allow about a week for mail time, so I decided to send my card to Robin Zander from the band Cheap Trick. His birthday is January 23rd. I've enjoyed their music ever since they started recording in the late '70s, and it's one of the few bands I've seen in multiple decades (in 1978 with REO Speedwagon at the Checkerdome ) and almost 30 years later (in 2006 at Live on the Levee).
I found the address for his management company and sent the card off. Hopefully he'll receive it.