1. Don't wrap the gifts
Really, it's not worth it, whether the presents are going in your checked luggage or your carry-on. If your bags get opened by security, then all those presents will have to be unwrapped and that will take time. Besides, the presents will look a lot nice if you wrap them when you arrive (things tend to get crushed in your bags!).
2. Bring extra supplies in case of delays
It doesn't take a big snow-storm to cause delays. Even something as simple and relatively short-lived as a freak hail-storm can cause long delays when you're traveling by plane. Traveling in winter (AKA winter-holiday-season) means you risk more problems of this kind. Of course you can't prepare for every eventuality, but just make sure you bring some extra supplies like diapers, medication, formula, snacks, etc.
3. Pack clothes that do double-duty
Depending on where you're going, traveling in winter can often mean that you need to pack a lot of bulky winter gear: winter coats, snow boots, ski pants, and so on. To make things easier, it's good if you can pack gear that does double-duty. For example, boots and jackets that are snow and rain proof. And if you can wear your jacket for "just around town" outings, that's even better.
4. Arrive in good time
I'm a bit obsessed with being on time in general, and being at the airport with a lot of time to spare in particular. During the holiday season, you might very well experience longer lineups at all airports, so arriving in good time is a great way to protect your sanity, especially if you have younger children in tow.
5. Tag your luggage
Unfortunately, airlines and airports sometimes misplace or lose your luggage. This can happen anytime you travel by plane, but if you get stuck in an airport with delayed and cancelled flights aplenty, the lost luggage can pile up. Make sure you tag your luggage, outside and inside!, to increase the chances of getting your things back, even if they are misplaced. For more tips on how to make your luggage safe, read Better safe than sorry: 10 luggage & packing tips.
6. Charge all your electronics before you go
It's always a good idea to charge your electronics before traveling of course, but during the holiday season when you might get stuck in an airport or on the runway for long periods of time, this is a real must. Make sure any tablets, laptops, and cellphones are fully charged so that you can use them for communication, and to entertain your kids.
7. Make sure you have space in your luggage for gifts received
If you brought some gifts with you, you probably have some space in your suitcases for a few gifts at least. Also, for those of us who have kids, it's a good idea to remind family and friends that you have to be able to fit any presents the kids get into a suitcase. (There are a lot of very nice presents that just won't fit easily into a carry-on or a suitcase!)