Where are you going? If it's the Caribbean then yes, I would suggest wearing a tee-shirt while snorkeling. What really gets burned are your shoulders because that's what is most exposed to the intense Caribbean sun. You burn much more easily in the Caribbean.
How do I know? From experience. I blistered my shoulders in Cancun. Of course that was 23 years ago...but I still remember!
Sometimes on snorkeling excursions they make you wear a lifevest (you inflate it only if you're in trouble). In that case your shoulders are covered so you're okay but if you really burn easily, why take a chance and ruin your vacation.
And by the way, it's actually a very good question!
Renee - The better half of RobRen :-)
Carnival - Spirit: Alaska (August 8, 2007)
Carnival - Miracle: Exotic Western Caribbean (April 9, 2006)
Royal Caribbean - Explorer of the Seas: Eastern Caribbean (January 2005)