1. Invest in a decent, portable humidifier. After waking up every morning for three weeks with a bloody nose, I went straight to the nearest mall to pick up a humidifier. Traveling for months on end in over-heated buses and living in hotel rooms with tightly shut windows and dry, hot air will give you cracked skin and bloody noses. It will also put you at risk for developing bronchial infections, which spread like wildfire on a tour of 60+ people. Get a humidifier for your room and solve these problems. I bought a portable one for around $30 USD at Target, and then bought a European one for about $40 USD when I went abroad. I run it constantly in the room, dry it out the day before we pack up for the next city, and travel it in my luggage.
2. Buy a practical winter coat. You're on an ice skating tour, not a fashion runway. Get a long coat with a hood, and make sure it's stain-resistant and won't get damaged if you roll it up and stuff it in the back of your lockbox.
3. Leggings. They're light to travel in your suitcase, and you can layer them under your other pants.
4. Bring a pair of cold weather boots. Dragging yourself to the venue on slush-covered sidewalks at 7:30AM on a Saturday morning will be more favorable if your feet are warm and dry.
5. If you're going to Europe, bring whatever cold medicine you like with you. You will get sick. You will not want to go searching for a pharmacy in the middle of the night in whatever country you're in when you're sick. There might not even be a pharmacy anywhere near your hotel if you're staying on the outskirts of town near the venue. Many of my coworkers have ended up at the hospital in need of basic cold meds they could have just brought with them. I would also suggest bringing along some antibiotics from your doctor back home.
6. Buy a good facial moisturizer. Wearing ten pounds of show make-up, and constantly wiping it all off will further dry out your skin. Find a moisturizer that works for you and use it religiously.
Above all, enjoy holiday hot wine and hearty winter soup, and think summer thoughts :-)