From reading many British childrens’ books while growing up (many written in the early to mid 1900s), tanned skin was usually called “brown”. It meant tanned white skin. Not the dark brown of of for instance African, Arab or some Asian skin.
Tolkien was using “brown” in that sense.
But Tolkien's useage is different. The whole Harfoot group of Hobbits was described by Tolkien as naturally brown skinned. The Fallohides were described as fair. This had nothing to with tanning - it was their natural colouration.
Before the crossing of the mountains the Hobbits had already become divided into three somewhat different breeds: Harfoots, Stoors, and Fallohides. The Harfoots were browner of skin, smaller, and shorter, and they were beardless and bootless; their hands and feet were neat and nimble; and they preferred highlands and hillsides. The Stoors were broader, heavier in build; their feet and hands were larger, and they preferred flat lands and riversides. The Fallohides were fairer of skin and also of hair, and they were taller and slimmer than the others; they were lovers of trees and of woodlands.
- JRR Tolkien - Prologue, The Lord of the Rings: The Fellowship of the Ring
Tolkien was using brown in that sense.
The Barefoot Boy
John Greenleaf Whittier
Blessings on thee, little man,
Barefoot boy, with cheek of tan!