Beer conditioning in a cornie will clear naturally as yeast particles fall slowly to the bottom (flocculate). This can take a while to do, sometimes many weeks. Finings typically isinglass or gelatine cause the suspended yeast particles to clump together and flocculate more quickly, giving you a crystal clear pint. Most commercial brewers of real ale will add finings to their casks when they fill them, so that their beers will clear quickly in the pub cellar before serving. Lager manufacturers like to filter their products even advertising the fact on their tins, but at home this is not easy to do.
I found Harris Beer Brite gives excellent results and is quick and cheap to use.
http://www.harrisfilters.com/fining.htm
1 packet (around £1) dissolved in about 250 ml water (use a blender if you have one) will clear a cornie very quickly, especially at low temperatures. It also has the advantage in this weather of helping remove any chill haze that may form if your cornie is in a garage, as are mine. At 2 degrees it is possible that the beer will be hazy because of natural protein strands in the beer joining together at low temperature. The haze will clear as the beer gets warmer again and it doesn't affect taste, but I like to serve a pint that is clear in the glass.
Its really all a question of personal preference. Some guys don't drink with their eyes, and if it tastes good its ok. My mates tend to comment if I serve them a hazy pint. They still drink it and come back for a second , but I like to serve clear if I can.