i swing my arms mostly when i walk, but sometimes i stop doing it. it looks pretty creepy when a person is walking without swinging their arms, almost robotic. i guess the way the mind perceives this is the same as those features that go into the uncanny valley. you become less human by not swinging your arms when walking.
i sometimes try and see if other people notice it and try to interpret their expressions when they see it. it would be interesting to get data on this.