Don't know why I missed the connection, but hazel is called filbert in the US, and is widely grown for its nut production, particularly in Oregon and Washington. In fact fresh filberts or hazelnuts should be appearing in grocery stores in a couple of months.
I can find sources of the wood on the net but I haven't found any description of its properties but one site said it was similiar to almond wood. If so, it's strong, nails, glues and stains well, good shock resistance, acceptable as a gunstock wood but very little color or figure.