It is but you need both a big hunk of mass and a way to detect the neutrino interactions inside it. Ice Cube is shot through with detectors. One of the OG detectors measured the particular isotope created during interactions.

https://en.wikipedia.org/wiki/Homestake_experiment#Methodolo...

The Super-Kamiokande has photomultipliers staring at a bunch of water looking for Cherenkov radiation resulting from neutrino interactions

https://en.wikipedia.org/wiki/Super-Kamiokande

None of these are much of a practical option with the moon.

You need to have the reaction mass to make use of. Most neutrino detectors use special chemicals in custom tanks, IceCube uses antarctic ice. You would need not just mass but ice or water for a neutrino detector, ideally highly compressed optically clear ice. The only possible candidate in the Solar System that fits that bill at present is Europa. Though it's possible that similar conditions might also exist on Mars (we know there are sub-surface glaciers, but we don't know how deep they go or how pure the ice is. And potentially some of the large sub-surface oceans (on Ganymede, Enceladus, etc.) might work too but we know even less about their properties.

Not all detectors were optical so if you found a moon made of, say, dry cleaning fluid, you'd still be good.

Each detector has a limited range. And only works well in certain mediums, generally water or water ice. Even if the Moon was solid ice, we would need to surround it with detectors, as well as drill a huge number of holes all the way through it and place detectors (probably hundreds of thousands or millions) in each hole.