If you're willing to brave the cold, stargazing in winter can be a very interesting hobby. Stargazing is sometimes more practical in summer, but different constellations appear at different times of the year. Stargazing in winter will give you a completely different set of constellations to look at, providing some variety. Most of the planets are also visible in winter (although they are a bit harder to catch because they move).
One of the biggest advantages of winter stargazing is probably the lack of bugs. Summer nights in Illinois tend to be rife with mosquitoes, and those can be immensely irritating when you're sitting in one place looking through a telescope.
Before you start stargazing, it helps to have a sky chart of your area so you can figure out what you are looking at. A sky chart basically marks the constellations that will be in the sky in a particular season, and you can match what you see in the sky to what you see on the chart. This
is a website where you can create a sky chart for your area. After you create a sky chart, you can either look at the sky with a telescope or without. A telescope also helps with seeing planets, and if you like, you can look at the moon. Make sure to use a moonlight filter; the telescope will focus the sunlight reflecting off the moon and it can be blinding.
Most of the constellations you can see are visible during other seasons, but there are a few notable constellations visible only in the winter in the Northern Hemisphere. One of the most well-known winter constellations is Orion. This constellation is named for a hunter in Greek mythology, and it can be most easily spotted by the line of three bright stars in a row. These three stars are Orion's "belt." In the "sword" part of the constellation, the Orion nebula can be seen, and you can get quite a good look at it with a telescope.
Another winter constellation is Cetus, the sea monster. Cetus is possibly one of the largest constellations documented, and it resembles a whale. The Latin classification for whales and dolphins, cetaceans, comes from that same word.
It is also fun to focus on planets in your telescope. With enough power, you can focus enough on Jupiter to see its stripes, and possibly some of its moons (although its moons will appear as very tiny dots). You might even be able to see the Great Dark Spot if you focus enough. Saturn is also visible sometimes, and you can also see its rings with a good telescope. Uranus and Neptune are a lot harder to see, but they are possible to catch if you have a big enough telescope. You will have to move the telescope a bit as you watch planets, however, since they move rather quickly across the sky when you're looking at them.
No matter what you're looking at, winter stargazing is a good way to add variety to what you do during winter, and is enjoyable despite the cold.