If you live in a home with no insulation or central heating, even a fall morning or evening can feel frighteningly cold. Muscles that should be warm when you practice have to be massaged quickly in the shower or after sitting and watching TV, or you feel you have to do aerobics before you get going with yoga. Aerobics!? You didn't plan an evening of aerobics did you you!? You wanted to do yoga! So, how are you going to keep your body warm, so that you can safely enjoy a full yoga practice in your cold home in a place where even running a space heater is too expensive?
Tai chi, whatever style you practice, can be done just about anywhere and in any weather. With the exception of Yang style that requires a wooden floor to do turns, tai chi can be done on the beach or in a park. Assuming you are preparing for a yoga practice in a cold apartment, a 10-15 minute tai chi long form can be done without any prior warm up because of the slow and gentle speed of the practice. By the end, your body will be slowly warmed up, and prepare you to start a yoga routine with slow deep breathing and a calm and meditative state of mind.
Another warm-up I like to do are what yoga teacher Lucas Rockwood calls gravity poses. These are a series of yoga poses designed to increased flexibility through the use of gravity and deep breathing. Most of these poses are held up to 5 minutes. I like to do about 15 minutes of these even if I have done tai chi on a typical day. Because of their use of gravity, they are in fact perfectly safe to do without a warm-up - though they are even better after some kind of warm-up. I think they themselves are a good warm-up too.
In Japan, I also have a Kotatsu, which is a Japanese floor table with a heater under it. A Kotatsu is great to warm your legs, so that once you get out of it after about 10 minutes, you could comfortably start a yoga practice. Alternatively, a hot shower or even better yet a bath - would have the same - if not even greater benefit to make sure your body is warm and that you are in a relaxed and comfortable state to practice Yoga in a cold space.
My apartment also has an air-conditioner in the living room area which fortunately doubles as a space heater. Set this going and the room will be warmer, and at least more comfortable to work-out in.
Something else I tried recently was putting on heavy layers of clothing for 20 minutes. By heavy layers, I don't mean putting on 6 or 7 sweat pants over one another. What I mean is buying a winterized pair of snow pants. Uniqlo and other clothing stores have affordable winter clothes that are light, but specially designed to trap heat. A hoody is also great to wear over a long sleeve shirt for a while around the home. I also have a neck warmer. This is basically a tube you can wear and pull down to warm your neck.
After you feel warmed up from wearing extra or special winter clothes, change your pants to a pair of full length sweat pants. If you feel you need to, you can wear dance or exercise tights under these. Some people also like to wear leg warmers. Make sure you are wearing socks to keep your feet warm. Keep your hoody on until you feel warm enough to take it off. After taking this off, keep it close to your yoga mat along with a small blanket. You will need them during slow cool down times and the blanket is a must during the final rest or savasana time.
A note of caution is that you will need to be extra cautious to listen to your body. You may not be able to get your legs as warm as you could in a heated space. You may therefore need to go easier on your stretches. I also find that my body is not as good at telling me that it is thirsty in colder weather. Drink regularly before the practice, and if necessary during the practice. Drink something warm if possible as warm drinks are best for the health of your throat.
Be your own boss. When you practice at home, the DVD teacher is just a guide. You are your own real teacher. The controller is your friend and should be used as needed. In a cooler room, you may sometimes need a longer time to move into a particular position you find challenging. I have tight hamstrings on my right leg for example. In cooler weather, I sometimes need to pause the DVD player to give myself more time to get into a wide angle stretch.
Finally, in a cooler temperature, a regular sleep routine is more important than in warmer seasons. A tired body, in my experience, is more susceptible to chills and infections (such as sore throats or irritated sinuses) in cold weather. Don't push yourself as much in your training if it is getting late. But, you will need to keep yourself moving throughout your practice without breaking much (if at all) or you will find yourself cool down much faster than in warm weather.
Be safe!