I have several friends who have skied at Alyeska, all in late February or early March (they all live on the East Coast, so it's a similarly lengthy trip). From what they've told me, you go to Alyeska because you want to experience Alaska, not because you want an epic ski trip. Winter is low season, so it's cheaper to visit, and there are less crowds (going to Alaska in summer is like going to Yellowstone National Park or Banff). And, overall, the resort itself is not crowded, so you pretty much have the mountain to yourself.
I don't know what level skiers you are, but Alyeska is really an intermediate's mountain as far as terrain is concerned. My friends all said that experts have some good drops but the real challenge of Alyeska is the tremendous variety of terrain and snow conditions from top to bottom. Snow may be groomed, cut up or untouched. Sometimes it's powder at the top and mashed potatoes at the bottom. Since those conditions affect terrain for all ability levels, you should feel comfortable skiing in variable conditions to really enjoy it. If the snow is not fresh, it is very technical and difficult skiing. While my friends didn't say as much, it sounds like Alyeska can be a bit like Whistler because of it's low elevation and location on the ocean. Perhaps someone else here can confirm or deny that.
When they have whiteout or flat light conditions (which apparently is often enough), you can't ski a large portion of the mountain because there are no trees to provide definition. On those days, you do something else: dogsledding, visit museums, wildlife cruises, sightseeing, and so forth.
As someone else said, it gets light later in the day. However, by mid-February, Alyeska gets more daylight hours than other resorts in North America. Lifts open at 10:30 AM and normal closing time is 5:30 p.m., but on Friday and Saturday nights from mid-December until mid-March, the lifts remain open until 9:30 p.m. By late-February/early-March, temps average about 30 degrees F, so it's fairly warm (not as cold as you might expect in Alaska).
If you're really into dogsledding, go to Alyeska at the same time as either Fur Rendezvous (late Feb.) or the Iditarod (early March). Everyone I know said both of those events are worth making the trip for. Also, you'll probably see Northern Lights, which are truly spectacular so farth north.
I hope that helps some!