whicks,
I've never seen anything specifically mentioned about handheld gimbals at any of the sites I've visited in Italy. For the Colosseum the rules seem to focus mainly on entry rather than photos.....
"Please note: for security reasons it is strictly forbidden to enter with backpacks, camping, bulky bags and luggage/trolley. Medium and small size backpacks can be introduced and must be screened by metal detectors, as any other bag. They must be opened and visually inspected by the security."
Tripods and Monopods are an issue for many locations as they impede the movement of visitors. Handheld gimbals don't have that same problem as they're kept close to the user. You'll probably find that entry will depend on the security staff that are working at the time you enter the site. Some security staff may not even know what the gimbal is used for.