Last night, I bought a bike. My intention is to bike to work 2 to 3 times a week. Looks like about 440 calories can be burned one way.

The bike comes in on Saturday. They had to order one because they don't keep my size in stock (I'm 6'4").
Today, it got cold. I now have to figure out how to stay warm while biking.
This will also be good for my puppy, as he loves to run but I don't want to run the time he demands because I don't want to hurt my joints.
How cold is cold? Up here I ride regularly all winter. Get a Gore-Tex jacket for the outer layer, wear a micro-fleece underneath, and if necessary a wicking underlayer like polypro. Make sure everything is breathable, you will get a worse chill if you sweat. Gore-tex is also a great windbreaker, and remember you should be getting up a good speed most of the time.
Make sure your bike is fitted properly. I won't try to advise you too much via internet, but whichever style bike you bought, you want a riding position that is fairly stretched out forward, with ass back in the saddle. This will keep your shoulders from cramping up on a long ride, it brings more muscles into play and is better exercize.
Worst position is very upright. Nice for a ride through the park is all. You will cramp up after a long ride, hard on the lower back (like sitting upright in a bad office chair all day) and you tend to just use your weight to push the pedals down instead of exercizing your leg muscles.
Use toe-clips or cleated shoes that snap into the pedals. This is intimidating for inexperienced riders, but if you want the most out of the exercize you will be using all the muscle groups in your legs and get more balanced muscle strength. Conciously apply pressure through the full 360 degrees of each pedal stroke, with both legs, and it will become automatic after a while.
If it bothers you to be strapped into the pedals, go to an empty parking lot on the weekend and DON'T LOOK AT YOUR FEET, just practice going in and out of the pedals 100x while you ride in circles.
Good handlebars for commuting, even on a road bike, are flat mtn bike bars with bar extensions that give you a forward riding position. Sometimes called "steer horns." For the longer part of the ride on a clear road, you can change position regularly to relax your arms and shoulders. In traffic, bring your hands into the bars and the bar ends will protect your hands if you get a car door opening. Bar ends are actually a great protection in traffic.
Not sure how bikes are treated on the roads in your area, but generally, take up some space. If you ride too close to the gutter/shoulder, cars won't change lanes to go by and will crowd you and clip you. Keeping into the lane also gives you room to go to the right if someone is coming up behind and isn't respecting your space.
I'm always happy to see someone take up riding, it's great exercize and a great life, but take care of yourself on the road.