I'm surprised this is coming to City Council - the industry is based in Council Speaker Christine Quinn's district, and I've always heard they're tight. Still there's a big push to ban them now from the animal rights people. The main sponsor, Tony Avella, represents Northeast Queens, which is about as far from a tourist area as you can get (although the main sponsor of the industry bill, James Gennaro, represents a similar district right next to Avella's).
Riding the horse drawn carriage is really one of those things I've never understood. 34 bucks for half an hour to do what exactly? See Central Park, just in a slower, smellier way than walking?
My bet is that a full ban doesn't go through, but the city starts genuinely cracking down on infractions next season. The carriages aren't supposed to leave the park, and the horses aren't allowed to work in bad weather (extreme heat, cold, storms and dangerous street conditions), but these - like many traffic laws in New York - are sometimes taken more as a loose suggestion than a law. You can generally find the carriages in Midtown before 9:00 PM (when they're allowed), and out in all sorts of weather - especially if it's December, the biggest tourist month of the year.
The public hearing is set for January 29th - any bills affecting the tourist industry usually get brought up in the winter to avoid disruption and changes during the season.