Steppers are the worst case for battery power -- they draw full current all the time they are in use. Motors with worm gear drives and linear actuators hold their positions without power, and come in all imaginable sizes.
The most difficult parts of the project are the door opening and locking arrangements. Only you can determine the most suitable mechanisms, and then you will need to determine the "effort" (force/torque) it will take for a motor to move the selected mechanism. Buy a motor according to the required torque and speed.
Since this is all custom you may have trouble finding examples. However, chicken coop doors are a popular topic, and many examples have been posted on this forum and elsewhere. Try searching for "diy automated chicken coop door", for example.