Yes the cold weather can cause a drain on your cars battery and cause your vehicle to take longer to crank over due to the battery becoming weak in cold weather.
The cold weather slows down the chemical reaction inside the battery which makes the battery go low or even go dead.
If you're having trouble starting your vehicle during the cold weather you should make sure the battery is not too old and if it's too old go ahead and replace it.
Also you can install a trickle charger on the battery that you leave hooked up to the cars battery and then when the car is parked you plug the trickle charger in which keeps a slow charge going on the battery overnight or when it's sitting.
The trickle charger will keep the battery from being too low when you go to start your car.
Most car batteries will work good enough to get your vehicle started even in frigid weather but if the battery is a lower quality battery or an aging battery then the cold weather will do more draining of the battery.