The weather in ancient Greece, like the weather in most places, changed with the seasons. Greek weather also depended on whether you were in Northern Greece (near Thermopylae) or in Southern Greece (near Sparta). In the spring, it would be pretty rainy, especially in Northern Greece, and the plants would get green and leafy. The temperature would generally be in the 60s Fahrenheit (10-20 degrees Celsius).
Then in the summer, it would be hot and dry. Farmers would harvest the wheat at the beginning of the summer, in June. It hardly rains at all in Greece in the summer, especially in Southern Greece. In Northern Greece sometimes there are thunderstorms in the summer. In Northern Greece it would generally be in the 80s or 90s Fahrenheit (about 30 degrees Celsius), but in Southern Greece it could get up over 100 pretty often (over 40 degrees Celsius).
In the fall, around October, it would begin to rain again, and there would be storms. The temperature would drop into the 70s and then into the 60s Fahrenheit (25-10 degrees Celsius). This would be the time to plant the wheat and barley.
Winters in southern Greece are chilly and rainy, but not really cold. It’s pretty unusual for it to snow as far south as Sparta, though it does happen once in awhile. Most of the time in Southern Greece it would be in the 50s during the winter (about 10 degrees Celsius). You would need a cloak to be comfortable outside, but you wouldn’t need mittens. In Northern Greece, it would be colder, and there would probably be snow several times in a winter, though you wouldn’t have snow on the ground continuously. You would need a warm cloak, and boots, and mittens, to keep warm outside (In ancient Greece they didn’t have sweaters, because knitting hadn’t been invented yet).
This is basically the same as the weather in Greece today. It hasn’t changed much since antiquity, although with global warming, like everywhere else on Earth, Greece is getting a little warmer.
Learn by doing: compare the weather in Greece to your weather for a few days
More about the Greek environment
Greece the Land (Lands, Peoples & Cultures), by Sierra Adare (1998). Geography, climate, and more.
Ecology of the Ancient Greek World, by Robert Sallares (1991). Not easy going, but very interesting.