Then you need to research the more expensive RFID systems unlike the ones we generally deal with here which will read a RFID tag within perhaps 10 cm.
Point is, you probably do not need "ID", just a sense that the mower is in the vicinity. May be vastly easier to simply open the gate whenever the mower is actually operating.
Motor? Windscreen wiper motor perhaps. 
So completely irrelevant to this project. 