If you live in a part of the world that experiences significant climate changes throughout the seasons of the year, then the type of running shoe you may want to use could differ depending on the season. Running in the warmer summer months, and in the colder winter months are two completely different situations, and your running shoe choice should reflect this.
If you run outside during the cold winter months, then you are going to experience ground that is a lot harder, so you need shoes with ample cushioning so that you do not jar and injure yourself. The ground will also be more slippery, so you also need a shoe that provides your feet and ankles with sufficient support. Grip and traction will also be important, so you need to ensure the sole of the shoe has been designed with plenty of grip.
Some examples of running shoes for winter training
Adidas Supernova Sequence 6
Adidas have a wide range of running shoes, and they bring out new models every year. The new Supernova Sequence 6 offers a well-designed shoe that has some very innovative features that make it suitable for winter running. The cushioned sole of the shoe will actually mold into the shape of your feet, as well as providing plenty of support as you run on the harder ground.
The sole of the shoe provides a lot of traction, so is ideally suited to wetter and more slippery surfaces. The shoe also features air mesh uppers and synthetic overlays, which combined help to provide a very strong and sturdy shoe and allows your feet to breathe, which is essential no matter what the weather and temperature is like.