As the name indicates, winter tyres are tyres for the winter season or more precisely for winter weather conditions, which includes cold weather, snow and ice. Winter tyres are actually better than summer tyres as soon as the temperature drops below zero degrees Celsius. The main reason is that the summer tyres are not designed for cold weather and their tread pattern is not optimized for snow and ice. They have been designed for warm temperatures and the road conditions that you mainly will drive on during summers. This means dry tarmac and they are also optimized for heavy summer rain.
Summer and winter weather is so drastically different, both in temperatures and the surface you drive on, it is thus very difficult to design a tyre that can manage the full scope of both, especially if you also demand high performance. During the summer on dry summer roads, the rubber will have good grip on the tarmac. The rubber compound is optimized to give you the right balance of softness and grip while still having good tyre wear characteristics to minimize the wear. The tread pattern will make sure that you have good control and steering properties as well as short braking distance. The tread also takes into account good properties on wet surfaces, so that you can avoid aquaplaning while still having excellent wet grip.
When you then reach winter you will have a completely different designed tyre. You firstly have tyres that can handle cold temperatures while still remaining soft and flexible. Then the tread pattern has to be designed for snow, ice and slush. They also have to provide grip on these conditions. This is why you need to change to winter tyres when you approach the winter. You need tyres that have been optimized for the conditions and can provide the grip and safety that you will need. So why to change is quite clear, as it is actually dangerous to drive with summer tyres.
Since it is dangerous to drive with summer tyres, you will need to change the tyres before the winter weather arrives. Since the winter tyres are already safer than summer tyres was the temperature drops below zero degrees, you should already change when the temperature drops and don’t wait for the snow to arrive. This will improve your safety.