As snowshoeing is an outdoor activity we are exposed to varying temperatures and winds. There might be snowfall, or even rain. Keep in mind that the weather can change while you are out. Sometimes also quite drastically.
How to dress & what to bring
The basic principle is to dress in layers. How thick and many layers depend on the temperature.
Wool is to prefer close to the body. Wool dries fairly fast and feels warm even when moist.
The top layer protects you from snow, rain and wind.
Head, feet and hands
A warm hat for the head
A pair of warm shoes with higher shaft. It doesn't have to be a rough hiking shoe but it should have a decently thick sole.
Don't forget gloves or mittens
A small backpack is good as protection for some additional clothing.
You can also carry some hot drink with you.
A little energy snack per individual taste is always good to have.