Depending on how far you will be traveling, you might be just fine without any chains or studs. I don't have to travel farther than a couple miles on any lake I fish and I don't use chains or studs. It's pretty rare that there isn't any snow at all on the ice here. Even if there is very little snow for traction, it's not hard to drive a straight line and turn on glare ice, at least in my experience. Just take it easy, which you should do on the ice anyway.
I don't want chains chewing up my trailer, driveway or garage floor. So the minimal inconvenience of not having chains on the ice is worthwhile for me. And, I don't want to chain up after unloading my ATV on each trip. This is just my opinion and what works for me. Thought I would throw it out there - maybe you want to see how things go without chains before settling on it.