iirc, HA allows 2 bottles of wine to be brought aboard at embarkation. On subsequent port stops, they confiscate alcohol and return it on the day you disembark. And they charge A LOT for water and sodas. One way around that is getting a drink card. They will be available shortly after you board near the buffet. Some cruise lines and discounters will include this perk. My personal 'petty larceny' is to put a box or so of wine in my checked bag for use in the cabin, then order OJ with the above mentioned breakfast room service and use that and some sprite for a sangria in the cabin before dinner.
This business of getting a cruise for a low price is a bit of a mine field. We have said, "It might cost you $500 to get on a cruise, but you'll pay a LOT more to get off it." With the charges for drinks, shore excursions, 'mandatory' tips, charges by the minute for internet, specialty restaurants aboard, fancy coffee drinks, the mini bar, even water conveniently left in the cabin, all suddenly appear on the bill that is automatically charged to the credit card you produce when you board.
You CAN cruise on the cheap, but they make all the 'little extras' seem so innocuous and easy and cheap, 'you're worth it', and that drink-of-the-day with the cute umbrella and beautiful fruit in it looks so good- for only $7.50 (plus 18% gratuity) will add up by the time the cruise ends.
Jim