Hi Theresa,
Yes, you definitely can do quality interval workouts on a treadmill! One of my friends trained almost exclusively on a 'mill during the winter and ended up running a 2:35 marathon that year. Another friend (male)did intervals to train for the mile and ran a sub-4:15.
You can do almost any kind of workout (within the limits of your machine's speed, of course) but I tend to favor longer intervals and "hill repeats." I find the short, fast stuff (i.e., equivalent to 200s and 400s) just too hard to do between adjusting the speed, not losing my balance, and keeping track of the distance. Also realize that running on the treadmill will seem much faster than running outside. I can do mile repeats in under 6:00 outside but anything faster than "7:00" pace on the 'mill is too much for me. Be careful that you don't injure yourself by going too fast and screwing up your natural stride.
I much prefer using the track for shorter speedwork, although where I live, the track at the local community college is also open to walkers and children and navigating around those people can be lethal.
Also, I must respectfully disagree with Pete about running in the snow. I have two friends who really screwed up their hamstrings and lower backs by trying to run in the snow. You need to make sure that your body can handle it and that you don't have any biomechanical problems or muscle imbalances. Lots of people have no problem, but apparently back and hamstring problems are a bear to get over!