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Are you talking about hazelnut wood? which I'd bet would be a nice flavor like hickory.
Or hazelwood? which I think is like a sweet gum, with a five sided leave.
Didn't find hazelwood anywhere in the Woods For Smoking sticky nor did Google really produce anything helpful. I would think you could smoke with it but then again it may not burn properly or may have a lot of resin, I don't know.
I recently tried out smoking with birch, lots of folks weren't sure if birch was a good wood to use and it turned out to be great, though birch was on the list in the sticky.
I'll do a bit more looking around and see what I can find but hopefully someone will come along and offer you a definitive answer.
The reason I asked for clarification is that I thought hazelnut/Filbert was a common tree in the UK, but I remember hazel wood in the south USA being the same a a sweet gum. I would love to have some hazelnut wood it has to be great to smoke with. I was also thinking that using hazelnut shells for smoke would be good too.
Hazelnut trees don't grow very big, but they are a species that handles coppicing well, (ie if you cut the main trunk, multiple new trunks grow from it) - some farmers coppice a few to grow new straight sticks for their shepherd's crooks & walking sticks. I doubt that it'd be difficult to get permission to harvest a couple of trunks.
Read an article in Bushcrafter Magazine (a british 'survivalist' magazine without the guns I guess you could call it) that recommended Hazel wood for smoking. Tiem for trip to the nut-wood!!
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.