For that to be possible, the tree would need to go dormant first, it would have to be deciduous, and it would have to drop it's leaves before placing in the refrigerator. It is far better, with far less headacbes and losses, to work with something appropriate to your zone, or something that will survive indoors.
Starting off with something that is, by default, going to be exceedingly difficult is a very quick way to become completely frustrated, even to the point of dismissing the bonsai hobby, as so many do, as impossible.
What zone are you in and which species are you worried about keeping? There can be some alternative species to consider.