Search the area and follow the tracks. You'll see a horse cornered by a group of zeds. After you fight them (I had 3 runners and 3 walkers) you can interact with the horse. Offer him food - and then you can take him with you!
MUST HAVE ROPE!
You can encounter Empty Street a second time, however the second time there will be nothing here.
If you have no food left, the option "offer him food" will not appear, making it impossible for you to take the horse.