I wouldn't say chains are a must. I've had mine for 8 years & sure was glad I had them the 2 times I needed them. I've always thought of chains as one of those things I'd rather have & not need than need & not have !!
The conditions in which you will be riding the ATV will dictate whether you need chains or not. On bare ice you will need chains or you can stud the tires with some screws. The condition of your tires will factor in also. A quality set of new tires will serve you well.
Evaluate the situations/conditions you will be using the ATV in out on the ice & go from there. If your ATV doesn't have a winch, I would suggest getting one. My winch has got me out of some sticky situations more times than I care to think about.
Good luck to ya & have a great season on the hardwater !!