Well, composting would give you a way to use waste products and have them turned into something useful. A sustainable system is closed in the sense that you need to buy as few resources as possible and produce as little waste as possible. Your system just keeps turning, like a perpetual motion machine, with you feeding off the system. Composting your waste is a way to reintroduce it into your system and "closing the loop" so to speak.
In your case you are not part of a self-sufficient sustainable system. All you can do to live more sustainably is take measures to have as little negative impact on the system as you can, that is reduce the number of things you need to buy and reduce your waste (or give out your waste in a way for the system to make it reusable, which you do by separating your trash). A direct way to control your impact on the system is to
Reduce your requirements for input and reduce your wasteful output.
For example, there are many people who use their balcony as garden, be that just herbs, vegetables (like runner beans on poles, potatoes) or bees. To overcome the climate conditions, you could consider turning your balcony into a greenhouse by adding a layer of glass, which in itself would reduce your input (gas/electricity for your heating) and reduce your wasteful output (CO2 emitted for generating the heat). Again, a balcony vegetable garden would reduce input (groceries, new plastic bags) and wasteful output (used plastic bags, CO2 emissions from the supermarket trucks, etc.).
Composting makes most sense when you use the compost yourself, but even if you do not use it yourself, your gardening neighbour would probably be happy to receive good compost, or even just good food waste. This way you make sure that your food waste doesn't just get burned, which would be a real shame. Food waste is so close to being something so useful...
Compost is useful where something grows, be that lush foliage, or just shrubs. In your climate, it is admittedly not easy to live sustainably, because you need or want things which your environment does not provide.