I live in Northern New York, and I would really like to continue jogging outdoors, because I hate the treadmill at the gym. Is it unrealistic to go jogging in 20-40 degree weather?

We don't have much of that around here. Slick pavements would be the bigger risk, I think; put a scarf over your mouth to help warm the air. And stay on a short course where you can get home safely if you decide it's not working, rather than a long trail where the far point is too far.

I love to run outside in the cold weather. Here in NYC the winters can be really cold, and especially windy. The lowest temperature that I can run outside in is about 35 degrees, after that it gets too cold and windy. I run with a scarf over my mouth/nose, and a headband and hat. I look funny, but hey, there are less people out there anyway!

Happy trails!

Oh, I do, I do! I trained for my last marathon in some horrid weather. I hate the 'mill! I live in Utah. Just invest in some good wicking fabrics, gloves, hat, good jacket. Wear plenty of layers. I have the Marmot Precip Jacket and it's great because it has 'pit zips so you can vent when you need it, but I can also pull the hood over and I can zip the jacket up all the way so it protects my face as well. If I get too hot I can unzip the pit zips, or even tie it around my waist. I see them on e-bay al the time for decent prices, aorund $50.00 for a very high quality jacket!
underneath that I usually wear a fleece vest that covers my neck, and some type of high performance material top made of poly-propylene or other good warm but wicking fabrics. I wear two tops plus the vest and jacket when it is between 0 and 20. Above 20 I am usualy in just the long sleeve shirt (North Face El Capitan zip neck), vest and jacket, with hat and gloves. For my legs I wear a good thick pair of tights.
runners world website has this great "dress the runner" feature that can be very useful as well.