How much energy do you need?
In four months you spend $7500, so assuming you heat using natural gas, that would indicate a consumption of about 19,000 cubic meters. At 10.8 kWh per cubic meter, we're talking 200,000 kWh; in four months that's an average power requirement of 70 kW.
Can the Sun help?
Reasonable solar output in New York is around 5 kWh/m2 per day.
Four months is 120 days, so solar panels will give you 120*5 = 600 kWh per square meter. To reach 200,000 kWh you would then need 340 square meters, i.e. double the surface area of the pool.
The cost of such an installation can be quite high.
Do you really need all that energy?
Now 70 kW divided by the surface is around 430 W, which seems to indicate appreciable evaporative losses throughout the day. Evaporative loss is a function of three parameters (water temperature, available surface and airflow temperature and speed). You may get considerable savings by:
covering the pool with a black "solar blanket" when not in use. If you do not already do so, this should cost around $1,000 and can save you from about one third to one half your current energy budget (even more if you don't use the pool every day and leave it uncovered). That's around $2,500 each year, and a good solar blanket will last 5 years easily.
surrounding the pool with a tall fence, hedge or windbreak mesh that will lower wind speed and reduce losses when the pool is in use.
Using electricity, which is one of the "noblest" forms of energy (as it can be easily transformed in any other form) to generate heat (which is the basest form) should be a last resort. Photovoltaics lose around 85% of the available energy before even starting.
Much better to directly tap into solar heat.
To actively heat the pool, depending on the distance between the pool and the green area, my suggestion would be to use either a water recirculation system (possibly connected with the pool pump) or an insulated circuit with heat exchanger (requires additional, low power pump) between the pool and a solar heater plate. This is basically a long black UV-resistant PVC tube where pool water or heat exchanger fluid (water plus glycol and other substances) slowly circulates, and gets heated by the sun. Thermal efficiency is near 80-90% compared to the 10-15% of solar panels, i.e. you can get by with a surface four times smaller: half the size of the pool instead of twice that. Also, the cost is way lower, and the components are next to worthless (PVC tubing, come on), which means they're really unlikely to attract unwanted attention even in not-so-safe neighbourhoods. Insurance costs are proportionally lower, and repairs can be done by anyone.
Here you can find more info, including DIY instructions.
(Note: you need to drain the tube completely during the cold months, lest it be damaged by freezing).
Electricity banking, heat pump
Both methods are "multipliers" for the efficiency of a photovoltaics system. With electricity banking, you sell (or "store") electricity into the utility grid in those months when you don't use the pool at all. Then when you have need of the pool, you divert the PV output to the pool, and can supplement with energy from the grid - that you "stored" in the past months.
Unless you get special tariffs, the best you can hope is to get the energy at the same price at which you sold it; this is pure banking. But the electricity was produced in the coldest and darkest months, so the split won't be exactly 8:4; more likely something like 50%-50%. So the energy you can get back is of the same order of magnitude of that which you produce in the summer. This then doubles your efficiency, and you can use a PV surface half the size: i.e. the same area of the pool.
Same goes for a heat pump. A heat pump uses, say, one unit of electricity to "move" some units of heat from the environment into whatever you need to heat; the electricity also adds to this heat. Typically you get another doubling of efficiency, even if the heat pump requires maintenance; so your heating costs won't be really halved.
Combining electricity banking with heat pumps, you could then get to heat a 160 m2 pool with 80 m2 of solar panels. It seems to me that it's still better to go with solar heating tubes, even without factoring in maintenance costs, permits and installation.