It depends on where you're going and from where to where. Generally, I did not find the air conditioning to be too chilly, and I could control the temperature in my stateroom as far as the degree of air conditioning or not.
I will say that even in somewhat warm/tropical areas - it's not quite as warm as you might expect when you're out on the open sea. It's not cold exactly, but because of the breezes and so on, it's not as tropical as you'd expect. More balmy, a little cooler and so on.
Thing is? As soon as you're in port, in a warm-ish place, it gets a lot hotter than you've been used to for however many days you've been at sea getting to said port. All of a sudden, the ship is in port, standing still, and it's not so breezy anymore. Can be a lot hotter all of a sudden.
Meanwhile, I didn't notice extremely cold air conditioning either - you're wandering around on deck, heading for breakfast or lunch, or maybe off to sit by the pool or what have you - most of this is open air and no real air conditioning to speak of. It's not the same as being enclosed on a plane. The only place I actually noticed the air conditioning was in the fine dining areas and specialty restaurants. Oh, and my stateroom too - but I could always turn the a/c down or off if I wanted to.
All of this is to say that if you're off to a tropical destination on a cruise, it won't be as hot as you expect while at sea, and further - the a/c isn't frigid, because there are so many open areas.
Where are you thinking of going, and when? My parents just returned from a Hawaii cruise from the Pacific Northwest area. It was cool-ish on the way down and on the way back, and warm-ish/tropical while in Hawaii - but never too hot at any one point. On the contrary, Mom went to Europe a couple of summers ago in the middle of August, and while it wasn't too hot on the ship, it was very hot (for her) in the numerous ports they stopped at.
Figuring out jackets depends on where/when, if that makes sense. I've been on two cruises, both to tropical areas, and did not use a jacket at all except for one formal night when I opted for a dressy suit instead of a dress. That said, something like Alaska or Northern Europe would be a whole different story!