Yes go in the winter time.  I'm going on a 7 night cruise and after it was all said and done we ended up paying about 389 a person.  That's not how much we paid in the beginning but we booked as an early saver.  That means if the price of our cruise goes down we get money back.  However once your cruise is paid off it goes as an onboard credit to you sign and sail card.

Cheap cruises would be from October-early March.  Cruises are high March and April due to spring break then go back down slightly in May but go back up in June.

If you do cruise in the summer keep in mind that is hurricane season so make sure you get insurance.  Without insurance you are out money if your cruise is canceled.  You'll get your money back for the cost of the cruise but not for travel expenses to get there.