My older nephew will be 6 this year and he started wrestling when he was 5 last year. However being that my brother-in-law and my sister have both watched me wrestle for so many years and I have been coaching/officiating for the last 4 years, We were all able to come to a conclusion on his status as a wrestler. Although he is quite young he was able to attend practices. There were some nights when he absolutly wouldn't pay attention or didn't want to be there. In that case he would be told to either sit on the side or Joe would just take him home. In other situations he would do just fine. He went to about 4 or 5 tournaments and placed at 2 or 3 of them.
I think that biggest thing to remember is not to put any pressure of them to win at that age. Obviously they are going to lose and many of them are going to cry because they feel like they aren't "winners" That is where the parents have to come in and be completly supportive. Too many times I have seen the parents of little kids at tournements say negative things to their children after losing. Things like "I can't believe you did this..." Or "Its your own fault for not doing ..."