Mountaineer and legal officer. Born in Husabost on Skye, the son of a tacksman and farmer, Nicholson studied theology at University of Edinburgh, but did not enter the church. He was eventually to turn to the Law, appointed an Advocate in 1860. In 1865, he became Assistant Commissioner for the Scottish Education Commission and went on to inspect schools across the Outer Hebrides. He then served as Sheriff of Kirkcudbright (1872-85) and then Sheriff of Greenock (1885-93).
He died in Edinburgh. He is known to have revised the Gaelic Bible, but is perhaps best remembered for giving his name to Sgurr Alasdair ('Alexander's Peak') in the Cuillin of Skye, which he was the first to climb in 1873.