Sure, but they are far more accurately a state regional intelligence and military apparatus.
Just to be consistent, if Hezbollah are a terrorist organization, then Mossad absolutely are as well, along with tonnes of Intelligence Agencies like the CIA, MI6 etc.
I don't like the idea of claiming that States apparatus themselves are "Terrorist organizations" because it opens a pandora's box of states just accusing eachother of being terrorists, for pretty frankly, standard espionage. I think Terrorist orgs genuinely have to be largely clandestine sleeper cell loan shark groups, acting for the purpose entirely to conduct terror. Hezbollah just doesn't match that, it's a uniformed army and intelligence agency functionally, of elements of Lebanese state and supported by Iran.
Also personally, I just do not understand, why Westerners, would ever give a single iota of a fuck about Hezbollah or Hamas, when Hezbollah has been fighting against the Islamist Wahabbi nutcases that keep driving through Christmas Markets in Europe. Without Hezbollah kicking them in the nuts, ISIS would have 100% won the Syria blood bowl and the West would be seeing a Terror wave unlike any it's ever experienced. Hezbollah and Lebanon, hell even Hamas and Iran, are pretty "moderate" by Middle Eastern standards. The Gulf States are basically Islamist Wahhabi psycho North Korea tier outside of their potemkin cities. Saudi Arabia can just slam Airliners into American Skyscrapers and Iraq and Iran get the blame for "Islamic terror".