Martian winters are more brutal than even the coldest place on Earth. It can plummet as low as -143 degrees Celsius (-225 degrees Fahrenheit) in the negligible atmosphere of the polar ice caps, whereas the coldest temperature recorded on Earth was -89°C (-129°F), in Antarctica. It gets so cold on Mars that the carbon gas in the atmosphere freezes at certain times in the Martian calendar, causing the atmospheric pressure to plunge.
The main problem with Spirit and Opportunity wasn’t the cold, though – it was that they were solar-powered, which meant that during the dark periods they went into a state of hibernation with little or no activity. However, Curiosity has an independent power source, so it won’t have to work around the same constraints.