Edit: Thanks, ltk. I wasted my typing on YOU!
Make a Winamp playlist and make a shortcut to it.
Then, as luv2chill said, just tell Windows Task Manager to run that shortcut at the appointed time.
This works quite well, I've done it myself! For a bit of variety in your alarm make the playlist of ALL your .mp3 files and leave Winamp on random. It's nice to not wake up to the same thing every day.