The letter, dated Thursday, suggests the carriages be replaced with environmentally sound classic cars, the New York Daily News reported Friday.
"Trading in horse-drawn carriages for eco-friendly cars is a responsible way to modernize the industry while keeping that Old World New York charm and creating alternate jobs for horse-drawn carriage operators."
Huston, who has been living in New York while filming NBC's "Smash," wrote the letter to Quinn on behalf of People for the Ethical Treatment of Animals.
"It's surprising to me that a city known for its progressive spirit still allows this cruel and dangerous tourist trap," she said.
"Several accidents over the past few months highlight the immense safety hazard and lack of regulation of this industry," the letter said. "At the end of 2011, within just a couple of weeks, two horses collapsed in the middle of traffic and one nearly hit several taxis on 59th Street."
2014: The Year in Music [PHOTOS]