The 60-year-old has joined hands with animal rights organisation People for the Ethical Treatment of Animals (PETA) India to fight for the cause.
While several people enjoy horse-driven carriage rides in the Marine Drive area of the metropolis, Aman wrote: "Both tourists and locals are saddened and appalled by the plight of these horses. These gentle animals are often malnourished, injured and ill yet are forced to haul carriage loads heavier than their bone-thin bodies can bear."
Zeenat's letter has been addressed to BMC commissioner Sitaram Kunte.
"Mumbai has so much to offer, but the pathetic spectacle of horse abuse is the first thing that many tourists see, and it taints their impression of our great city," she further wrote.
Aman joins a growing number of celebrities, including Hema Malini, John Abraham, Jacqueline Fernandez, choreographer Sandip Soparrkar and his supermodel wife Jesse Randhawa, who have expressed support for the cause, and asked the government to ban horse-drawn carriages.