There was no garden on the Temple mountain in Jerusalem because of a space limitation. Gardens of private persons were available on the Mount of Olives. The owner of the Garden of Gethsemane might have given permission for Jesus to use it for night prayers.
PRAYER OF JESUS IN THE GARDEN
After the celebration of Passover, Jesus went with the eleven apostles to the Mount of Olives to pray and gain spiritual strength before his passion. When Jesus and companions reached the garden, Jesus took only Peter, James, and John closer to him where he prayed. These three were dear to him and they were with him on special occasions, like raising to life the daughter of Jairus (Mk 5:37) and the transfiguration of Jesus (Mk 9:2). Even though Jesus requested them thrice, “My soul is sorrowful even to death. Remain here and keep watch with me” (Mt 26:38). They failed and fell asleep. The triple request was a sign of how fervently he needed their support. So, in the great distress, Jesus was alone.
Jesus said, “Foxes have dens and birds of the sky have nests, but the Son of Man has nowhere to rest his head” (Mt 8:20; Lk 9:58). The Son of God, who created everything in the world, had to depend on others for night rest, that included houses and gardens. The humility of Jesus and his solitude in the acute time of distress are clear in the prayer of Jesus in the Garden of Gethsemane. Those who work full time for the kingdom of God might also face similar situations.