I agree, walking really does help stabilize my mind and body when I am feeling stressed. It is so simple that I sometimes forget how effective it really is. This is especially true when the weather is nice and I can walk outside.
I remember when I was in high school I often felt really under pressure, with no where to turn for relief. The very best thing was walking my dog, at the end of the day. Together we would tour the neighborhood. And I almost always returned home feeling more sane and calm.
I could go into all of the scientific reasons about how this works but who cares, it does work.