There is no need to deploy the whole thing on the mast. Just put there a preamp with 1090MHz filter and run a coax to house (where network and 120V is available). You can build a small shed (or a big box) at base of the tower too.
I am running 150 ft of RG6 coax to my AirspyMini/Pi3. Power over coax.
PS: Personally I am not using the T available in the dongle, voltage it is too low to allow for voltage drop at the preamp side. I have a variable voltage (steps) source in my house, set to send 9 V with an injector over coax and a 5V stabilizer up at the antenna before feeding the preamp.