Moorhouse was born in Yorkshire, England, and baptised on 18 December 1825; the oldest son of William Moorhouse, a magistrate, and his wife, Ann Carter. He trained as a lawyer, entering as a student at the Middle Temple in November 1847, and was called to the Bar in November 1860. After working for a time in London, he moved to Lyttelton, New Zealand, with his two brothers (Benjamin and Thomas) in 1851. Soon afterwards, he moved to Wellington, where he resumed his law practice.