You could use RegisterForAnimationEvent() and see if any of the animation events for the character fire. You will need to use ConvertHKX on the animation files, and look in the behavior files for the actor. For example:
moveStartmoveStop
... are two events that you can listen for. However, I do not know if those ones actually fire. In my testing some don't show up when you output the current eventName from the OnAnimationEvent() block.
As for animation variables you can use GetAnimationVariableInt/Float/Bool on the character to determine if he is in motion. For example these may help:
SpeedDirectionTurnDeltaSpeedWalkSpeedRun
... Those are floats.
For example in my footprints mod I listen for FootLeft and FootRight. Those only fire when the player is moving so you could use those as well, but there are more "continuous" methods available to you like the animation variables.
http://www.gamesas.com/topic/1360112-full-dump-of-all-animation-variables/
http://www.creationkit.com/RegisterForAnimationEvent_-_Form
http://www.creationkit.com/OnAnimationEvent_-_Form
http://www.creationkit.com/GetAnimationVariableFloat_-_ObjectReference