Answer:
Yes. There are no dietary restrictions during Hanukkah other than Kosher, which is observed year-round.
Ashkenazi Jews will not eat rice during the Passover festival; an 8 day festival during the spring. (Only 7 days long in Israel.) See http://www.answers.com/topic/kitniyot for details.
Jews will not eat anything on their 6 fast days - see http://www.answers.com/topic/ta-anit for details