This is because this type of clothing (compression clothing) is thin enough to let your skin sweat and breathe at the same time while also being dense enough to protect your body from the weather. With specialized form fitting cycling bib shorts that are made to avoid chafing and rubbing on the thighs, also sporting a set of mesh suspenders to help keep them secure to the cyclist's body, and a padded bottom allowing for a more comfortable ride.
These types of cyclist clothes are usually made from polyurethane polymer which is also anti allergenic and what most sports clothing is also made of. These include jerseys the aforementioned cycling bib shorts, gloves made to protect the hands, socks, jackets, vests etc...
With this type of clothing there is also no limit to when you can go cycling. Any season is fair game when your clothing can both warm and cool you depending on need. For the colder seasons there are arm and leg warmers, jackets which can be both water proof and provide insulation for those extra cold days during the winter.
But something everyone should wear when cycling is protective equipment such as helmets, gloves, knee and arm pads which can save you from fractures and broken bones. And because safety is a priority in every sport and activity one should never go off cycling without taking some safety precautions for the worst case scenario. By informing someone or simply going with someone could save your life in the possible occurrence of an accident.