No, the tilapia wouldn't survive the winter there... You don't want them to. If they did, they'd over populate and make a mess! The fact that they die each winter is an up side in their use. They are annual stocking deal.
Keep it simple for now... Start with feeding for this year. As you start to learn more about your pond and learn more on the forum, perhaps next year you can attempt to fertilize. IMO, fertilization isn't the easiest thing to do PROPERLY. You can make a real mess or waste a lot of money. Feeding is pretty simple... Either consitantly hand feed or buy a feeder to do it for you. Use a high quality feed and you will see some great results. Plus, most fisheries biologists wouldn't recommend a feeding and fertilizing program in the same pond...