tvc,
I think the battery life will vary - dependent upon which sight you bought, how bright you use it at, and if you turn it off after hunting. I believe the newer ones have much better circuitry to conserve battery power. I have a Burris and a Millett, and after several years, have not replaced a battery yet - but, I turn mine off after I am done hunting, and I haven't used them very heavily. I also always carry spare batteries when hunting - but I am known for carrying two of everything, except maybe rifles and treestands. I looked at Cabela's website and I think that they had an Aimpoint with a claim of 50,000 hours of battery life. That's astounding to me, since there are about 8800 hours in a year.
In order to get a better idea about the sight you bought, maybe call the the company or there will be some info in the owners manual? In general though, I believe that most of them will go a full hunting seasons and longer with no worries. I also imagine cold weather might have an effect - seems to with all batteries.
Good question - I am wondering too....