How is it possible to know about climates of the past? One way is through ice core samples. Long-standing glaciers in Greenland and Antarctica have been collecting ice in a seasonal pattern, and a carefully gathered core will reveal these layers. Inside each layer, microscopic air bubbles contain various isotopes of gasses, some of which are more likely at certain temperatures.
Another way is in the fossil record. Fossils of plants or insects in a certain layer of sediment indicate the approximate temperature at which that sediment formed. Another way is lake bottom sediment cores which contain fossilized pollen grains of plants which had sunk to the lake bottom each year. Again, the types of plants can indicate what sort of climate was occurring at that time. These and other methods cannot tell us anything specific about past weather, but they can certainly reveal generalized periods of weather over years or centuries.