Yes, it is entirely possible.
You can drive a unipolar (5 of 6 wire) stepper with some simple buffers like the ULN2004. For a bipolar (4-pin) stepper motor you will need a Quad H-bridge motor control shield (2 H-bridges per stepper).
You might want to use small geared steppers because you don't need really high speed but you do need enough torque that you don't miss steps.
You might also want some kind of index sensors so that you can recover from a power failure. Without some way to sense a 'home' position you won't be able to get to an absolute position, only relative.