It very much depend on some important features of the urban infrastructure.
I gather that we are considering an apocalyptic situation and that much of what makes society work has broken down. This will pose some problems when it comes to making a living in the broken cities, most importantly in this regard when it comes to food production and waste management.
- To have a feasibly large-scale production of horses you don't just need land, you need farmland to produce the feed required. And considering what I assume will be an equal absence of industrial farm equipment like harvesters and tractors the land will have to be worked by more primitive tools and those tools would need to be produced somehow. It is entirely unlikely for people to just come across plows that can be pulled by horses. So they would need to not only make them, but also know how to build them in the first place. This might take some time, depending on how lucky people are and what kind of information they have access to.
In early days it could be possible to bring up quite a few horses by feeding them off the land, but this isn't feasible for large scale production.
- Horses also need to eat while traveling and they need to eat quite a lot when working heavy loads. You are facing a problem of logistics when you bring the horses into urban areas if these urban areas aren't now teeming with newly sprung vegetation. You might need to bring energy rich foods like oats and these need to be produced at reliable quantities.
Another challenge for horses in a decaying urban environment would be the ground they walk on. If buildings are falling down and there is concrete blocks, glass and metal rods sticking out of things in the street it might be unsafe or impossible for horses to move forwards. Horses can move in terrain, but they are best suited for plains and grasslands. They are at risk for breaking their legs or tripping and falling if the ground is too messy with debris.
- The advantages of horses over scavenging motor vehicles might be many and varied, but they are unlikely to dawn on most people before the vehicles they have been used to for all their life isn't working anymore. Taking care of horses can be hard work and it requires time to learn how to do it in this new apocalyptic situation. Taking care of a motorcycle might seem a lot less daunting in the short-term. However if you did have access to a lot of horses in the first place with a large storage of feed so that you could keep them alive while figuring out how to make more feed for them.
It is worth considdering that horses are more than a mode of transportation, they are company, warmth and protection, and many people empathise with them easily. People admire horses, they have a lot of symbolic value. If somebody came across a horse in a apocalyptic situation they might bring it along simply because they didn't want it to die, and not because they thought it would be more practical as transportation.
I hope you find ways of making this work for the survivors of your story. But keep in mind that it might be better for the horses hooves to run down along side the highway and not on it.