Police horses are especially trained to deal with crowds. We were in NYC the night when the Iraq bombing started in 1991, and there were assorted losers demonstrating; a group of these cops on horseback galloped past, and they were an intimidating sight. When they started a program with cops on bicycles in my town, many volunteered because of the opportunity to exercise (they needed it).
NOTHING puts things into perspective like a HUGE horse with a cop astride, standing in front of one. I love'em. I wish we had more.
Cop on bike is FAR less intimidating, especially if the cops are wearing Bermuda shorts. But, their guns shoots real bullets, so I, for one respect the entire package, uniform, badge and gun.
Side story: we had a pound hound rescue (cutest dog in the world, but no training) and one day we were taking mutt for walk. He saw a horse and cop, his first ever. He was STUNNED with shock. He had never seen a horse before. Hahaha, doggie didn't move until horse was out of sight.
Jurassic Park.
The bike cops are not intimidating at all, just showing they knew they needed the exercise (there was no shortage of volunteers).
As for your dog’s reaction to the mounted cop, the Incas had the same reaction; in their initial encounters with the Spanish they supposedly didn’t understand the horse and conquistador were two separate things.