My ATV is registered as a motorcycle so from what I've read, passengers under 16 have to wear a helmet/protective eyewear. From what I've read about car seat law, 5 years and under must be properly restrained in a child seat. ARS 28-907. So could I strap the child seat onto my ATV rack and take my 2 year old son for a (very easy) ride around the neighborhood at the cabin. I would be very sure that the seat is attached properly.
Be very careful, are you planning on taking him on the road or off road only becuase different rules would apply, driving something on something that is not a "highway" or road has different rules but be careful if you harm your child or create a risky situation there is a variety of charges such as endagerment, child abuse etc, that you could face.