Every season needs a beginning or end. Most athletes will become better athletes by playing two or three seasons of sports. With Hockey, you really need to give up your fall sport though. After seven months you need to give your body ( and mind) a rest. Take at least a month or two off! You are not going to fall short of your potential by taking a break. That being said, if the kid wants to skate, let him skate! Summer skills are Absolutely essential to work on your game and give you an opportunity to focus on skills and MAYBE play in a tournament or two. Above all it shows commitment and helps build confidence.
It has been said so often; really depends on the individual and what their goals are.