Does the person's walking say anything about the person's cognition? This afternoon I've been observing people at a local park and came up with some observations that lead me to this question:

Can the person's gait (manner of walking) say something about the person's internal experience at that moment? I'm thinking of arousal and cognition.

For example:
Have you ever seen a businessman or an office worker walk? They walk with a purpose, quite energetically with the body slightly inclined forward. Is it feasible to say that when such walk is observed, the person is going somewhere, and may be tense?

A child may be running around with arms in the air, along an irregular path. Can it be said that such child is energetic and excited at that moment?

Two elderly people may walk very differently. One couple walks at a regular pace of 3-4mph, while another couple may push one foot in front of the other at 0.5 mph. Can this tell us anything about the differences in the mental activity that takes place within these people?

A person may be strolling slowly at &lt;1mph, observing the environment. Can it be said that such person is calm?

It appears to me that in the examples above, the person's mood/demeanor and  motion are connected. 

I'm interested if there's really any correlation between how a person appears outwardly and how the person feels? In other words, if one is tense and feels pressed for time, would one start to "walk with a purpose", as opposed to strolling casually?

Thank you for your input.
In terms of answering this question I will address the one final question;
I'm interested if there's really any correlation between how a person appears outwardly and how the person feels?  

A commonsense  answer to this question without any scientific research is; Yes.  All animals have non-verbal communication. Much of human communication is based on non-verbal factors. We ca interpret if someone is hostile, and unapproachable, or if someone is happy; from facial expression and body movements. A person's health and vitality is reflected in posture and gait.

Now scientifically:
There is correlation between how a person appears outwardly and how the person feels.
This question overlaps with interpreting body language and mood.  

In terms of gait:
There is extensive research on the effect of a person's mood on gait. The studies I have listed below cover aspects of normal gait, and how gait is analysed, to the effects of mood on gait.

I have quoted from the article mentioned by Jeff in the comments.


  The authors examined the relationship between cognition and gait
  velocity, performed with and without  interference, in elderly
  participants. Neuropsychological test scores from 186 cognitively
  normal elders  were submitted to factor analysis that yielded 3
  factors: Verbal IQ, Speed/Executive Attention, and  Memory. Regression
  analyses revealed that these factors were signiﬁcant predictors of
  variance in gait  velocity, but the relationship varied as a function
  of task condition. All 3 factors predicted gait velocity  without
  interference. However, the Speed/Executive Attention and Memory
  factors but not Verbal IQ  predicted gait velocity in the interference
  condition. These ﬁndings suggest that gait velocity and  cognitive
  function may have both shared and independent brain substrates. Future
  studies should explore  gait velocity and cognitive function as
  predictors of dementia and falls.


Gait
Mansfield, P.J., Newmann, D.A., (2009), 
Essentials of Kinesiology for the Physical 
Therapist Assistant, Mosby: St. Louis, MO.

Psychosom Med. 2009 Jun;71(5):580-7. doi: 10.1097/PSY.0b013e3181a2515c. Epub 2009 May 4.
Embodiment of sadness and depression--gait patterns associated with dysphoric mood.
Michalak J, Troje NF, Fischer J, Vollmar P, Heidenreich T, Schulte D. 

Can J Psychiatry. 1987 Apr;32(3):190-3.
Mood, depressive illness and gait patterns.
Sloman L, Pierrynowski M, Berridge M, Tupling S, Flowers J.

Neuropsychology Copyright 2006 by the American Psychological Association 
2006, Vol. 20, No. 2,  DOI: 10.1037/0894-4105.20.2.215
Cognitive Processes Related to Gait Velocity: 
Results From the Einstein Aging Study
Roee Holtzer, Joe Verghese, Xiaonan Xue, and Richard B. Lipton 
Yeshiva University