It's really not that difficult, unless you're like the woman I met on my last cruise who had packed one large suitcase just with shoes.
My husband and I did the trip around the horn last February, and each of us got by very well with our standard large check-in bag, modest roll-aboard, and small carryon, each. Most of the trip is in relatively warm weather; it's only the few days furthest south that you may run into serious cold and wind. I packed only two pair of warm slacks, figuring that pantyhose and wool socks under them would probably keep me warm enough; half long-sleeved and half short-sleeved jerseys, a warm sweater, and a really good windbreaker/raincoat. Other than that I took my usual warm weather cruise gear. As it turned out, the weather was unusually mild during our transit and I never even used the sweater. My husband actually went ashore in Ushaia in shorts, though I think he was the only one off our ship to do so and after all, we are from New Hampshire.