We don't really have a good understanding of global weather because we personally only witness a small part of it at any moment. Sadly, this doesn't stop many people from reaching conclusions about global climate change based on their local weather, but the best way to fight that is education. People must be informed about the difference between the global climate and local weather, or about counter-intuitive like the fact that now that cold waves are rarer, they seem worse because we're not as used to them, making us think things are getting colder ("Why is it so cold if the Earth is warming?")...
But the facts are that 2013 marked the thirty-seventh consecutive year of above-average temperature, that despite cold wave in US, December 2013 was the third hottest December since records began in 1880, and that out of 13,950 peer-reviewed scientific papers on Earth's climate published between 1992 and 2012, only 24 reject global warming.
One way to realize how different global climate can be from local weather is to take a step back and look at the whole. This great video shows all of 2013's weather over NASA's Blue Marble map, with commentary by Mark Higgins, a geophysicist at EUMETSAT: