What can I do to protect myself from the cold?

The effects on your body are worth serious consideration. 

The two major culprits are cold and wind chill. Cold is pretty obvious, but with the wind, at wind-chills of -25F (-30C), exposed flesh (ears, fingers, knees) can quickly freeze.  Skin will freeze or dehydrate and crack.

Here's my advice for preparing yourself for playing in the cold.

For your body:

1. Start by taking aspirin or similar fever reducer. It causes the capillaries to open up and keeps your outside warmer. This heating consumes a lot of energy, so expect to be tired, but you'll be able to play.
2. Cover you exposed skin with hand lotion. The oil/wax content prevents moisture loss allowing your skin to remain flexible and not crack- so put it on your ears and knees, too!
3. Use petrolatum or wax (e.g.,Vaseline or ChapStick) for the lips (to prevent chapping/cracking).
4. If your nose starts to run, do not sniff - blow. Many pipers have blown out their eardrums from getting ear infections. It can occur anywhere from a few hours to a few days later. Consider taking a decongestant. The potential consequences on your hearing are not worth the risk.

As far as dressing:

1. Wear a tee shirt, shirt, vest and/or sweater under jacket.
2. Wear athletic warm-up shorts under the kilt. (For even the most hardy, there's nothing like a chilly day to define the boundary between "tradition" and "stupidity".)
3. Wear  athletic socks under the dress hose and protective rubber overshoes for the gillies (to protect from mud/slush). 
4. As far as handware goes, I use three layers. I have a tube made of fleece which has a "slot" for my thumb and covers about the lower half of the hand. It's made by "Turtle Fur" and called a "snowcuff" . Then I put on latex gloves (to keep in the moisture and hold the snowcuffs in place). Wearing latex gloves while playing keeps wind away from the skin, prevents moisture loss and the flesh colored variety doesn't look odd at all at a distance of 15-20 yards or so even on television. Then I cover the gloves with white musician's parade gloves that I've cut the fingers back so that the latex is what seals the chanter. This combination leaves me plenty of finger dexterity and only my fingertips get cold. If anyone knows where I can get white latex gloves (dress latex!) please, let me know.
5. In a strong breeze, a safety pin from behind to hold both kilt aprons together may be advisable.
6. Consider a balmoral hat rather than a glengarry. It is warmer!

As far as your piping:

1. You will be affected.
2. Focus on simpler tunes that you know well.

Good luck!!