no there was not a desert in ancient greece.
There are no actual deserts in Cyprus as there are in the Middle East- the nearest you get to such a thing are large areas of rough white stony ground dotted with scrubby bushes, stunted olive and fir trees, and thickets of brambles. However, none of these are large enough to have names of their own- they are usually bordered by farmland or by housing development, Cyprus being a small country and needing to make maximum use of it's land area.
No there aren't.
Greece has mountains, is not in the tropics and has no deserts.
Pennsylvania has no deserts.
There are no true deserts in Japan.
Baklava is a deSSert (you eat it) in greece. There are no deSerts in greece. People often confuse dessert and desert.
There are hot deserts, such as the Sahara, Mojave and Kalahari and there are cold deserts such as Antarctica, the Gobi and the Patagonian Deserts.
Definitely Greece!
Greece had a rough land with lots of mountains. Egypt was flat with mostly deserts.
There are no true deserts in Britain.
Mexico has two major deserts - the Chihuahuan and the Sonoran. Both are subtropical hot deserts.