The melting of ice caps has more to do with global warming than the ozone layer. Ozone is depleted because of CFCs (a pollutant) and that lets more UV radiation hit the earth. This is the type of radiation that causes skin cancer.
Now, if you're talking about ice caps--the problem here is mostly carbon dioxide, aka "global warming". The planet has what is called "surface albedo"-- the amount of light and heat that gets reflected back into space as opposed to absorbed by the earth (think of black vs. white surfaces in the summer). If there is a lot of carbon dioxide in the atmosphere, the reflected heat doesn't go back into space, it stays in the air and warms the planet. This is "the Greenhouse Effect." It works the same way that the inside of your car heats up in the summer.
As you may be able to guess, ice caps reflect more light and heat than other places on earth. So, as temperatures increase and the ice melts, the earth doesn't reflect as much heat, which increases the temperature, which melts more ice, and so on.
Eventually, yes, the ice caps will melt. But don't worry--300,000,000 years ago most of the earth was covered in water, so it's not like everything will die. It might even be a natural cycle, and humans are just making it happen a little faster. In fact, Volcanoes have dumped as much pollution into the atmosphere over the years as people have. The truth is, we don't have enough information to know for sure IF it will happen or when.