Why does Omri bring Little Bear outside in the book Indian in the Cupboard? What dangers do they meet?

Omri brings Little Bear outside because the Indian wants to ride his horse on solid ground instead of carpet. After Omri has magically made the horse, Little Bear mounts him inside the cabinet, where there is very little space to maneuver. Riding diagonally inside the tiny cabinet to make maximum use of the available space, the Indian and the horse leap over the ledge at the front of the cabinet and land on the carpet on the floor. The carpet is too soft for riding, however; the horse's feet simply sink into it like soft sand. Little Bear expresses his desire for a more solid surface on which to ride, so Omri decides to risk taking him and the horse outside.

Omri takes the Indian and his horse to a beaten path of earth and small stones in his backyard. He is very much aware of the dangers the two little creatures will have to face in the outdoors, and is vigilant in keeping them safe. First, Omri calculates how fast they might be able to travel should Little Bear decide to try to escape; Omri knows that they would not be able to survive long on their own but figures that, even if they ran as fast as they could, he would be able to keep up with them. Then, he begins to worry about what might happen if a cat were to see them. He warns Little Bear to be careful, because of "mountain lions" which are "big enough to swallow (him) whole and the horse too." He then allows Little Bear to ride free, and is astonished at the Indian's bravery as he dodges stones that to him are as big as boulders, and navigates a landscape in which ants appear to be enormous and a small bird flying overhead is perceived to be a gigantic bird of prey (Chapters 3 and 4).