The best way to battle the challenge of changing weather between the seasons is to have two sets of tyres and change tyres between the summer and the winter season. This will allow you to have the best tyres for each season and the best safety and performance from the tyres. It is always difficult to design a tyre that can manage such a big difference in conditions. This is why you will need to change the tyres. During the summer you will need a much different tyre, a tyre that is performing well on dry and wet asphalt and can manage high speeds and have good cornering properties. The tyre should also have good properties for preventing aquaplaning.
A summer tyre would perform very poorly in cold and winter conditions as the rubber compound used in summer tyres is optimized for warm temperatures. This means that at low temperatures, the rubber would become very hard and would not be able to provide the necessary grip required during the winter. This is why you would need to change tyres to a set of winter tyres. Winter tyres have a completely different rubber composition. The composition is optimized for cold weathers, so that they will stay soft and able to comply with the road surface for optimal grip.
With winter tyres you can also choose if you want to have studded or non-studded tyres. The studded have metal studs protruding from the tread to ensure good grip. This will be the best option for icy surfaces. For the non-studded tyres, they use a unique tread design to create the grip on ice, which give you still good grip, but not as good as with the steep studs. When it comes to snow, both these tyres will perform good, except on tightly packed snow, which becomes almost like ice and here again the studded will be better.
This is the best option for making sure that you will stay safe all year round. The main challenge will be when to actually make the change. With studded tyres you often have restriction on the period that they can be used, but you want to make sure that you have them mounted on your car before the winter weather arrives, as it is not safe to drive without them on your car.