Also a good idea. PoE injectors/splitters have come down in price since last I looked, so that is a feasible option.
My concern is temperature: the mast is located outside and exposed to direct sun. It’s also located in the foothills of the Swiss Alps, so it gets quite cold in winter. I didn’t want to expose the Pi to that sort of environment, so I keep it inside the observatory and out of the weather/heat/cold.
I’ll look into an enclosure that could hold the Pi, PoE splitter, filter, and Pro Stick while still providing weatherproofing. Do you think it’d be necessary to get proper waterproof bulkhead ethernet pass-through adapters, or would it be reasonable to bring the ethernet cable up through a small hole in the bottom of the enclosure (suitably sealed with RTV) and plug it directly into the PoE injector inside the enclosure? The hold would be on the bottom, so gravity would work in my favor. Such pass-through adapters are handy, but also quite expensive.