Yes, it does get cold in Cyprus.
Not as cold as Colorado Springs, where we lived in the early '90s, but then again houses in Colorado Springs had excellent heating and insulation. They had to, when temperatures sometimes even got into minus fahrenheit. I didn't know such cold was possible other than in Arctic climates. We thought the UK was cold until we lived in Colorado for a couple of years.
But then, in the UK we consider it cold when the temperatures hit zero Celcius. Chaos ensures in England when we get a couple of inches of snow, as happens - maybe - once or twice a year. Schools close, traffic jams pile up, and the radio issues warnings not to go on inessential journeys. In Colorado, the schools didn't close until we had a raging blizzard and two FEET of snow. Even then the traffic was mostly fine, since the trucks with snowshovels and grit were out constantly during the winter.
We saw enough snow in our two years in Colorado to last a lifetime, and assumed that the climate in Cyprus would mostly be warm. I knew the summer would be too hot for my liking, but thought that the winter would be quite pleasant.
All right, so we've acclimatised. Just before Christmas when we were bundled up in warm sweaters and fleeces, there were tourists wandering around in tee-shirts and shorts. We think it's chilly when the temperature gets below 15C [which is 59F] during the daytime, and extremely cold when it drops to 5C [41F] overnight. Part of the problem is that houses are really designed for the summer, with high ceilings, marble or tiled floors, and good ventilation. In the house we were renting until July, none of the windows fit properly and the ceilings were 4 metres high (yes, that's 13 feet). The only form of heating was a kerosene heater in the central room, which took the worst of the chill off the house if we closed all the shutters (not that any of them fit properly) and the curtains.
In the house we've bought, there's gas-fired central heating that's very effective, but of course we don't want to run it all day unless it gets REALLY cold. So it's on in the early morning, and from about 5pm through the evening. It means we only have to wear about two layers of clothes in the house, and no longer feel our fingers icing over as we type on the coldest of days.
Moreover it's not all that cold outside. People often say how odd it feels at first to put on a jacket when coming in, and take it off when going out. I still haven't quite got used to this. Indeed, when I go for a longish walk, I feel quite warm by the time I get home so I take off my fleece. Only to feel chilly again half an hour later...