Two questions, what battery chemistry, and what's the temperature outside?
All batteries struggle in the cold, but NiMH have it really bad because they start at 1.2v charged instead of an alkaline 1.5v. So most devices think they are half dead to begin with. And the cold is going to make that worse.
My lock was never this bad but I now own an ostation charger with their lithium AAs and the battery life is great. The only downside is they are obviously using a buck converter to get 1.5v so there's no voltage curve to indicate when they get low, they just cut off when dead. If you rely purely on the smart features and don't carry a key as backup you'll want to set a reminder to change and charge them on a schedule so you're never locked out.