I live in metro Detroit as well. In many ways the exercise bike may be better for you. It puts a lot less stress on you knees than running and is easier to vary the intensity (important if you do interval-type training). However, some people prefer the change of scenery and variation with running outdoors, and you do have to bike longer and harder (through "spinning") to get to the same intensity as running because running engages more muscles than cycling.
A third option: on the days where there is no snow or ice on the road, ride a road bike outside! That way, you get the change of scenery and pace, but can stay relatively warm because your body produces so much heat riding. However you do need a proper bike with proper fitting and proper clothing and other equipment.