Hiking in the winter can be fun, but it also can require you to pay more attention because your safety is at greater risk.
1. Pay attention, making a mistake in a colder environement is more dangerous and often you are just at higher risk from the changed environment that you are hiking in.
2. Water and food are as important as they are in the summer and can be more important. The winter can dry you out quickly due to dry air and you have to work harder to travel the same distances which means you need to have plenty of food.
3. Make sure you have high quality equipment that is properly maintained. Having adequate clothing, and hiking boots is very important when traveling in snow or other winter condtions such as icey weather.