Is there an equivalent of the "citizens band" radio service in your
country?  If so, a unit mounted in a secure, weather-tight box and
powered by the 12v used for the gate motor might work.  You might want
to add a "press to call" button that actually turns on the radio and
starts a timer that will turn the radio off a minute or two after the
last transmission to reduce the battery drain.

You could add a tone detector to the audio output of the radio at the
gate, so that a specific tone (or tone sequence) would activate a
relay briefly to open/close the gate.

John