Virtually every kind of plant grows and many species of animals exist in moderate climates. Moderate climates are called "moderate" precisely because they are not extreme, for example, the hot, arid deserts of Arabia and North Africa and sections of the American Southwest (and this refers only to the Northern Hemisphere; much the same exists in the Southern Hemisphere), or the frigid extremes found in the polar regions, where plant life cannot be sustained and few animals can survive. Plants, of course, are living, breathing forms of life. They exhibit cellular structures unique to vegetation but not unlike that found in humans with respect to ability to survive in extreme temperatures. The very reason the world's rainforests are mostly located in equatorial zones is because it is the temperatures and levels of moisture present in the air that provides the conditions necessary for the growth and sustenance of such vegetation.
While certain types of plants and species of animals -- think penguins in the Antarctic and polar bears in the Arctic regions -- are capable of surviving in extreme cold, very few of the planet's animal species can similarly exist in such climates. Similarly, while some species of plant life can survive harsh climates, the number of such species declines in number the closer one gets to the polar regions. In short, most plant and animal life exists in moderate temperatures precisely because it is in such climates that the conditions are present to support such life.