Can I add a second playlist to my iphone 5?

I created a playlist called "Oldies 1" on my iphone 5. I created another playlist called "Christmas Music" on my computer. I have synced my phone twice but the "Christmas Music" playlist doesn't show up on my iphone 5. I read the help section but it sounds like I can only have one playlist at a time on my phone. Is this true? Thank you for your time.