No, the horses are also a PR move. When cops are in cars, they’re enclosed and so there’s a physical and psychological separation between the cop and people around them. Sometimes, you want this. But a cop on horseback has no physical separation and you can count on lots of people coming up to pet the horse. Bike officers have the same ability to interact, but don’t have the animal sidekick to help.
That’s not to say that horses don’t have functions other than PR, but the police departments have cheaper options if the only goal is crowd control.