Skipping the rests
It is not possible to skip rest breaks, as they are a fixed part of the workout. It is important for the muscle to regenerate between intense intervals. It is however useful to keep moving during rest breaks not only to prevent you from getting too cold but also to enhance regeneration.
During the breaks
In a workout with maximum intensity running, it is up to the individual to decide how they regenerate as much as possible. You can run at an easy pace, walk, stand still or even lie down. It is only the time of the intervals which is measured.
In workouts with medium intensity, you should keep running during breaks. You should run the intervals in a way that you will definitely manage to keep running at an easy pace during breaks.
For beginners or if you run a workout at a low intensity in general, you should walk continuously during the breaks.