Neutrino detection generally requires large volumes and large masses (for very large values of "large"), neither of which are as yet feasible for space based systems. The IceCube neutrino observatory, for example, makes use of a volume of ice that is on the order of a cubic kilometer (over 900 million tonnes). Suffice it to say, building cubic kilometer solid structures in space that weigh hundreds of millions of tonnes is outside of our engineering capabilities at present. However, within the next several decades this might be feasible.
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.
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.
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.
