The natural key unfortunately includes many features which are not “naturally grown” at all - see https://wiki.openstreetmap.org/wiki/Counterintuitive_keys_and_values#Typically_natural - for example every stormwater retention pond and every canal is “natural” in OSM.
So don’t let that stop you from using the common natural=wood tag.
There might also be regional variations in tag usage - can you share what country and/or province/state this is in?