After moving to the United States, Alexander accepted an invitation from his cousin in Chillicothe, Missouri, where he showed a talent for the business and was made a partner in the store in 1874.

During his terms as mayor, Boise's volunteer fire department was reorganized into a professional body, anti-gambling ordinances were passed and other city improvements were made.

In 1908, Alexander was declared the Democratic nominee for governor in a bitterly contested nomination process which required intervention by the Idaho Supreme Court.

In 1914, Alexander entered the gubernatorial race on a platform strongly supporting prohibition and limited government spending.

)[2] In 1916, Alexander was re-elected over his Republican opponent, D. W. Davis, by only 572 votes, the closest gubernatorial election in Idaho history.

Alexander continued to be an ardent prohibition supporter even though bootlegging became common practice in Idaho in the ensuing years.

Despite rampant anti-German hysteria in Idaho during the period, Alexander himself was never thought of as unpatriotic, even though he was born in present-day Germany.

In 1876, Alexander married Helena (née Hedwig) Kaestner (1853–1949), a Christian immigrant from Germany who converted to Judaism.