Hazel, being I assume the nut, is great for smoking.
Here in the US Pacific Northwest it is a native wood and my family has been using it as a favorite for many years. Like all nut woods it is a mild and fragrant smoke.
PNW smokers are traditionally more about smoked fish and jerky than "Southern style BBQ." and for the twelve hour smoke/dehydrate kind of smoking that we do, a mellower smoke is better.
Alder is native here too and a lot of people make a fuss over it as a smoking wood but me not so much.
I use filbert for everything, jerky yesterday, smoked salt and smoked garlic the day before, and pulled pork today. I will put bacon in right behind that pulled pork. It has been a big week for my smoker.
Good smoking to you- Brian Bray firstname.lastname@example.org