Some quick thoughts on the whole thing.
The ban itself: You can read the rationale for and against yourself. I personally don't think they should be banned, but I do think a few more rules are needed, and that the carriages shouldn't be allowed out of Central Park (except perhaps Central Park South) at any time.
The bills: There's two bills - a bill to ban the carriages and an industry bill raising the maximum rate to $54 from $34 for a half-hour, and establishing some new rules. I don't think the industry bill is perfect, but I do think the new rules are needed, and raising is fair considering it's been decades since it was raised. I'm actually kind of torn on this. Horse Drawn Carriages aren't like cabs - they're a novelty, not a basic part of the city or a serious means of transportation, and novelties don't need price controls. If someone wants to pay a million dollars to clomp around in Central Park at 3 miles/hour, who am I to say it should be illegal?
On the other hand, I can't stand how every entertainment-related activity in this town has doubled in price over the last 5 years, and seeing one more go this route kind of gets me in the gut a little bit. In addition, there definitely needs to be transparency in pricing. It doesn't so much matter what the price is, just that it's listed and room for shenanigans are at a minimum.
My personal solutions is that the price cap should be raised, but tipping banned. Aggressive solicitation of gratuities is one of the worst things about the tourism profession in New York (there'll be a lot more on this later), and the Horse Drawn Carriages are by far the worst offenders.
The Politics: PETA (the big sponsor behind the ban) was smart to go after a high profile, but small and unorganized industry. If nothing else, they'll get some publicity and fund-raising appeal out of it.
Avella is probably sponsoring this for much the same reasons - the chance to get some publicity, fund-raising opportunities, and volunteer manpower (all of which he desperately needs) behind his Mayoral run.
If I'm the Horse Drawn Carraige industry, I'm super-pissed at Council Speaker Christine Quinn as the entire industry is based in her district. Maybe there some politics or process involved I don't know about, but if your councilwoman's the second most powerful elected official in the city, you aren't supposed to have deal with bills to ban your entire industry.
The Prediction: There's no way this passes. PETA rallies, Avella grandstands, and the bill gets bottled up in committee. Eventually the industry bill passes but with some stronger regulations and maybe less of a price hike.