The only solution besides keeping them warm (impossible with a dedicated outside light, in the car, unheated garage..) is to switch to Lithium, Lithium has way better cold weather performance than lead acid, alkaline or Ni Cad. Better yet, a rechargable Lithium battery, Lithium Ion, is even better in extreme temps.
Living in a cold climate it is important to me that when I turn my light on it will actually "turn on". Lithium is the only way to go in that aspect.
As an example, I keep a MagLight permanantly mounted in most of my vehicles, in the winter I fully expect those light to turn on at half the output they would in the summer, and last half as long, if that.
When I buy new lights these days I look for ones that use 2 123A batteries, then use a rechargable 18650 Lithium Ion cell in their place. I have some original Pila batteries that are going on 5 years old, they get recharged every day and used continously in a variety of lights, they are still running strong.
AA batteries are easy to find, but quality ones like Lithium are very expensive and still can't compete with a good rechargable stick. Cost has dropped dramatically too, a good rechargable battery (lithium Ion) and charger will cost about $30, have an amazing 10 year shelf life and will outperform any other battery composition. Lithium has no memory, if you fully charge a NiCad and only use a bit of it then recharge the battery will eventually only deliver the amount you previously demanded of it. Lithium will not do that.
Here are a couple versions of very modern batteries.
Left to right, first is a rechargable 123A battery, second is primary 123A batteries, Surefire brand, third is a "Pila" stick, it is meant to replace two 123A batteries like the surefire ones beside it, cheap to use and can be charged as often as you would like. The two blue cells on the right are Chinease copies of the original Pila, had for about $10 compared to the $140 I paid for the pila. On top is a lithium battery charger, it will take any variety of cell from a single 123A to a Double.
Any light bought for a use above what an average guy would use it for will use Lithium cells, and for good reason, they deliver current when current is needed. They don't hesitate when it is cold and their self discharge rate can't be beat.
