i recall some cases on this and the answer was that it was available to the winner so its 2010 income, he just didn't get around to picking it up. sort of like you getting a paycheck in dec and not picking it up till january, its still dec income since it was available to you. Besides, they usually withhold taxes on these, so go with the year they are crediting the withholding for would be the easiest and most prudent thing.
when i win the big one, i'll pay any year they want me to, as long as the check clears. [have doubts about NY]