I planted a couple seedling hazelnuts on the farm, but they are too young yet for me to have bonsai experience with them. From Wikipedia and my seed catalog sources:
Corylus avellana is the European Hazel Nut, and one cultivar is 'Harry Lauder's Walking Stick', it is a contorted variety. They are monoecious, having separate male and female flowers on the same plant, so each plant has both male and female flowers. The flowers open in very early spring, well before leaves. The flowers are wind pollinated.
So with the early spring timing in mind, it is not unusual to see bud movement during a mild winter. They are very winter hardy, even if the weather turns bitter cold, they will bounce back. What will open first is the flower buds, leaves won't pop until later in spring. I would not worry about your tree, even if we do return to zero degree weather. Only flower buds will be affected.
More factoids from Wiki and random readings, Hazelnuts, Corylus, are self sterile. The pollen from one cultivar will not pollinate the same cultivar. So if the only hazelnut you have is the clone 'Harry Lauder's Walking Stick' you will never see nuts. But if you get a different cultivar, like any of the ones used for nut production, suddenly end of summer you will see that 'Harry Lauder' is loaded with nuts. Actually "Harry Lauder" is not a heavy producer of nuts, though it does make edible nuts. It can serve as pollen donor for nut producing European hazelnuts, Corylus avellana.
Corylus - Hazelnuts curiously are in the same family as birch trees and hornbeams, Carpinus and Ostrya.
Hamamelis virginiana - Witch hazel - This is the North American native autumn & winter flowering witch hazel. I have seen them on my farm flowering in December, after a few zero degree days, with several inches of snow on the ground. Very pretty actually. Though flowers are so small, they easily go unnoticed.
The curious fact is that despite the common name witch hazel, the genus Hamamelis has no relationship at all with the culinary Hazels, Corylus. They are two completely unrelated lineages of plants. Hamamelis is somewhat related to Loropetalum, not at all to the birches.