There is one overwhelming factor they need, a food source, many organisms live in polar environments but the overwhelming live in places with productive natural conditions. Either places warm enough to support plant life for part of the year or they rely entirely on the ocean as a base for the food chain, which makes for a fairly short and simple food chain. Living in the arctic is not that difficult for an animal, compared to life in general, finding enough food is. Otherwise it is just a matter of preventing the body tissue from freezing.
Plants suffer from several factor limiting their survival at the poles. low light, prolonged darkness, and temperatures cold enough to freeze all but the most resistant body fluids. This limits the size of the plants becasue they have little in the way of excess energy to use for growing to large size. The closer you get to the pole the bigger these problems become. Tree require a lot of excess energy, wood is literally made of sugar that could have been used for their metabolism. trees also can bee split and shattered by water freezing in the trunk.
An additional problem is lack of moisture if the environment never gets warm enough for a thaw there is no moisture for plants to utilize, basically adding the problems of an extreme desert to the cold and light conditions.
Of course asking about a specific trait or type of organisms will allow for a more detailed answer, but this should help get you started, you can try the polar ecology wiki for more ideas.