That's the question. Was it rather warm over the entire country, in the middle, or unbelievably cold?
The study of ancient climate is called paleoclimatology. The word "climate," incidentally, comes from the Greek word, klima.
There is a difference of opinion about the climate of ancient Greece. For a long time it was the common view that ancient Greece was a temperate, forested paradise with meadows, like modern France or Pennsylvania, a so-called "Arcadia" and that this was ruined by people cutting down trees. This traditional view has even been taken up by modern scholars, notably Thirgood in his 1981 paper, Man and the Mediterranean Forest. This idea is currently not as popular, however, and the most common view is that changes have been limited and due to small natural causes over long periods of time.
The proponderance of evidence, such as pollen studies, seems to show that the climate of the Mediterranean has gradually shifted to becoming drier. See for example, Bottema (1994), The prehistoric environment of Greece: a review of the palynological record. There is a clear shift of trees from deciduous to evergreen, even in areas unaffected by human activity. Evergreen trees like colder, more arid conditions than deciduous trees. This change is reflected in agriculture as well, the crops being grown now being somewhat drier crops than in ancient times.
This can be seen in Arcadia itself, in the Tripoli region of the Pelopponesus, which is still quite nice, but a little bit drier and more scrubby than it was in ancient times.
Thus, a common view is that the climate of ancient Greece was similar to its current climate, but somewhat wetter.
In terms of the range of climate in Greece is that it varies significantly because there are lots of microclimates, due to the presence of both ocean and mountains in close proximity. For example, in Elis, you can find grassy fields and oak trees, but in Lemnos is a desert with sand dunes.
The current land of Greece, has actually changed little when compared with the ancient land of Greece when discussing its climatic nature.
The land of Greece is a very mountainous country, though it is also one of the few countries in the world, that is both a peninsula, as well as a country surrounded by archipelagos-(East and West of the mainland, as well as the large island of Crete South of the mainland). Greece had and still has a unique geography, when compared with much of the European continent, though has a fairly similar geography with many of its Mediterranean neighbors.
Much of the Hellenic landscape in Pre-Modern, or more specifically, Ancient times, would have been annually temperate-(especially in the Southern and Central mainland, as well as throughout its archipelagos and the island of Crete). That is to say, most of Greece proper, would have closely resembled a place, such as the California coast-(from San Diego to San Francisco, as well as Catalina island). A country, whereby most of its landscape had little annual rainfall, virtually no snowfall and not frequently subject to some of the ravaging forces of nature and the elements-(except for earthquakes and the occasional volcanic eruption).
In other words, the climate for most of Ancient Greece, was moderate and temperate on a yearlong basis-(not so dissimilar from other Mediterranean lands, such as the majority of Italy, the nearby Turkish Aegean coast, the South of France-(both the coast & the Provencal interior), the Spanish coast and Andalusia, the Dalmatian coast in Croatia, as well as the Northern coasts of Morocco & Tunisia.
Northern Greece, however, was probably, somewhat different than the rest of the country. In the case of Northern Greece, it was perhaps more similar to its nearby Balkan lands, such as the interiors of Albania, parts of the former Yugoslavia & Romania. This region of Greece was prone to frequent precipitation, including snowfall, as well as cooler and longer winters, in places, such as, Mount Olympus and especially, its interior region. However, the yearlong climate of the Northern Greek coast was somewhat similar to the remainder of Greece proper
Overall, Northern Greece, was climatically less hospitable when compared with the more temperate climate of Central and Southern Greece-(both the mainland and its islands).