The original Latin version is "the plow draws the ox in reverse position," meaning the same thing - that is, to get things in reverse order. The Roman proverb was translated into English in 1279. Over time, the ox became a horse and the plow became a cart.
This expression, meaning to concentrate on the basics, may come from the furniture business. Back in the 19th century, brass-headed tacks were used in upholstering chairs because they don't rust the way iron or steel tacks do. In taking a chair apart to reupholster it, a craftsman might say that he was getting down to those brass tacks.
Another theory has it that country store merchants hammered brass-headed tacks at intervals into fabric counters to measure yardage of cloth, and got down to those tacks for the sale.
SOURCES: The Encyclopedia of Word and Phrase Origins, by Robert Hendrickson; Brewer's Dictionary of Fact and Fable by Ivor H. Evans.