The positioning of the arms during body weight squats affects your center of gravity. Therefore the only difference in arm positioning is the stabilization muscles involved. This difference however is very minimal and won't have any noticeable affect.
When I perform bodyweight squats, I prefer having my hands out in front of me. This is a personal preference since I find that when I'm using correct form, most of my weight is sitting on my heels and therefore I have the feeling of almost falling backwards.
This feeling is typically cancelled out when I have weight added with the traditional weighted squat style seen with barbells. Due to this, some people like to practice or warm up for weighted squats with the hands behind the head position so that the have the correct feel. The hands near the neck position (when holding the barbell) is an important roll in weighted squats since it tenses the muscles in your back such as your traps which creates a groove for the bar to sit in nicely and stops it from shifting around.