After building a stable, talk to Torben resting by the river. One of the three types of horses will be given as a gift.
Maybe there are some uncompleted events with merchants and Gunnar before the expansion of the village. Take a stroll through various places where you can meet them, such as the wagon from your home to the village, the vacant lot next to the village tavern, or the riverside rest area. I wonder if anyone didn't get a horse...