You have several sub-problems that you need to investigate.
1) The main problem is signalling a cell phone at 500 feet (150m). The normal method that could be used to connect Arduinos to cell phones is bluetooth, and that does not have the range. There are consumer radio devices that can get up to that range in optimal conditions like OpenSourceRF (http://www.opensourcerf.com/), but you would then likely need a second device that attaches to the cell phone that can say when the signal occurs. If you can put repeaters between the Arduino and cell phone, you could use things like IEEE 802.15.4 or Wifi signals to send the message (IEEE 802.15.4 would need a device that attaches to the cell phone, if the phone has wifi support, you might not need an attachment to the cell phone). Finally, your main hope would probably use a cell phone connection on the Arduino. You can get GSM shields that plug into Arduinos that use a SIM card from a GSM cell phone and allow it to communicate. In the USA, only a few providers use GSM. Obviously, you would need to factor in the cost of a cell phone connection. I imagine those pre-paid phones would be the best way for a limited project.
2) You mentioned winter conditions, but you did not mention how long the Arduino has to run in winter conditions. You would need to build/buy an enclosure for the Arduino/battery. There are a lot of choices out there, but be sure when you buy it there is room in the enclosure to house both the Arduino and battery (I recently bought one that was a little too narrow inside for some of the gear I wanted to put in it).
3) In terms of the winter, note, that ALL batteries have reduced power capacity in cold weather, so it likely means you need to plan for more batteries to provide the power. If you are planning to run on a single AA battery, you would need to boost the current up to what the Arduino can handle (3.3v or 5v, depending on the model), and I suspect your runtime would be measured in minutes in cold weather. A single rechargeable AA battery provies 1.2 volts, while the non-rechargeable alkaline battery provides a nominal voltage of 1.5 volts (though the alkaline voltage dips as the power is discharged).
4) In terms of cost, if you are just starting out, and don't have an electronics kit, you will need to budget for things like wires, breadboards, soldering irons, etc. If you have a lab at school or a maker space, you might be able to use their facilities.
Frankly, the simplest way to solve the problem is get an Android smartphone, and write an Android app that does the sensing, and sends a text message when the event occurs (http://developer.android.com/index.html). You might be able to use an iphone as well, but I don't know how easy it is to program an iphone if you haven't paid for a developer contract.