Some absolute essentials when going to colder, drier climes:

from my Sydney trip

1. Conditioner for your hair is a must. It eases static, makes sure you don't get hat-head if you wear a hat, and you can go without combing or blow-drying. I use Sunsilk/Organics, the pink one with yogurt, weighty and smooth.
2. Lotion to prevent skin dryness and thus eczema or other kinds of dermatitis. Currently I am using a lovely gift from Jan, from Bath and Body Works, a raspberry vanilla flavour. My mistake was not getting a manly one for C, thus he also smelt equally yummy, not necessarily a bad thing.
   
3. Moisturiser for face, more than usual. Normally I use Clarins Multi Active Day Gel for day, but in Sydney I doubled up with Clarins Extra Firming Concentrate before the moisturiser itself. For night I used Clarins Multi Active Night Cream, after using Clarins Hydra-Care Mask, which I leave on for 5-10 minutes while catching the nightly matches in the hotel room.
   
4. If you don't moisturise enough, or if you have eczema like I do, then it is wise to bring some betamethazone valerate cream, otherwise known as steroid cream. It gets rid of rashes, skin flakiness and redness. Available only through a doctor. OTC only offers hydrocortisone, a milder and in my opinion less effective version.
5. Since it is dry, consider washing your clothes because it will dry overnight. Even socks and scarves. Then you can bring less. And leave the space for shopping!
6. Always bring a shawl. It can be used as a blanket (on planes), a pillow (when rolled up), a scarf which can be tied in many ways, and of course, as a shawl. Plus it dries faster than woolly scarves. Just beware the static.
   
7. Hand-moisturiser is important for the plane rides, to prevent said static, or at least, reducing it. I am currently using one that Jan gave me too, from Denmark. Small green tube like a Lion toothpaste-tube.
8. Bring water bottle where ever you go! Hydrate, hydrate, hydrate.