They sell suitcases too, so don't worry for that! December is usually warmer than february. And what you pack depends a lot of what you do. If you stay all the time in the hotel, if you plan to visit the island (the North is a lot cooler and don't you dare even think about going up to the Teide without winter gear! ), go out in the evening, ... What I usually pack for my boys: 4 beach shorts, 4 bermudas, 3 jeans, 5 t-shirts, 4 sweatshirts, 1 jacket, flip flops for the day, trainers for the night, and of course swimsuits. My DCs surf so we take wetsuits and one fleece each for when they come ice-blue out of the water. And don't forget a beach bag. I take as well a couple of ikea blue bags. Not trendy nor smart, but I always end up being the one who carries all the beach stuff (towels, water, book, cream, sweater, food,...) while the DCs carry their board, and the ikea bag is just perfect.
We go to tenerife every year for Christmas. I always take: short for the day, long for the night. I may be surprisingly hot some days and unbelievably freezing some evenings. The good news, is I buy a lot of stuff there as there is a nice benetton Outlet in Playa de las Americas. You won't feel cold in the hotel just outside if you go for a walk near the sea.
we've been to lanzarote in feb and its pretty warm during the day - shorts and tshirt weather, but during the evenings its jeans and fleeces. but guess its a slightly different time of year, and adjacent islands.
i can;t get my head around what the weather will be like. For the daytime will we be in shorts and vest tops, shorts and t shirts, cardigans? And for the evening could 8 yr old DD for example get away with wearing tights without being too hot? (she's just been given a new pair of sandals as an early christmas present but i think without tights she'll get blisters).