This list is not complete but rather items I find useful and that people often neglect to bring. For example, I am not including waterproof pants which every list from the touring company will include but I do include a neck gaiter, one of the critical pieces of equipment to have with you). I mark with an * those items I consider so important that I carry two of them South with me in case one gets wet or lost during a cruise.
Neck gaiter *
Warm hat *
Walking sticks [More and more passengers are carrying them but remember when traveling by zodiac you must keep your hands free, so ideally affix your walking sticks to your backpack or carry them on a strap securely over your shoulder. Remember also, that if you have them in your hands and you make a landing in a zodiac, these items are very dangerous and, if you are not hurt, you may well injure a staff member or one of the crew.]
Mitten gloves (half finger gloves with mittens that pull over hand)
Sea sick patch (Transderm Scop)(scopolamine)[Put in your airplane carry-on]
Watch (waterproof) that attaches to outer clothing
Lanyard (1 or 2) with detachable ends
Carabineers (2-3) not climbing grade, for cabin keys or swipe cards to monitor shore visits
Shirt (with pocket) worn just inside parka (to keep digital camera on lanyard)
Fanny or back pack. One that fits your gear to take ashore. Pack it before leave.
Bright color preferred (to distinguish you from other people when ashore)
If unable to walk easily, a cane that doubles as a chair (like golfers carry) or a small fold-up stool.
If not a birder, a monocular. Good binoculars can be had for $300. [I have no vested interest, but an ornithologist colleague recommended Nikon Monarchs.]
If a casual birder and you can afford $900, Leica 10X42 Ultra lights
Maybe a travel vest, useful for wearing on ship or on shore just under your company-issued parka
A second belt for your pants so that you can leave one belt in your shore pants
A fleece vest. Amazingly warm, takes up very little space
Keep in your shore backpack all the things you will need on shore and leave all this material in the bag, rather than having to pack it each time you go ashore:
Extra pair of gloves
One additional layer you can put on if you get cold ashore
Room in the bag to put one layer you take off when you are ashore
(my experience is that people then to over dress rather than under dress in December and January)