noun
one-horse carriage; single-horse drawn vehicle
Refers to a carriage or cart pulled by a single horse. A somewhat specialized term, more common in historical or descriptive contexts.
昔、一頭引きの馬車が街を走っていた。
Long ago, one-horse carriages ran through the town.
この絵には一頭引きの荷車が描かれている。
This picture depicts a single-horse cart.
二頭立て means 'two-horse (carriage)', using 立て instead of 引き. 一頭引き is less common and more specific to pulling by one horse.
Compound of 一頭 (いっとう, 'one head (of an animal)') + 引き (びき, nominalized form of 引く 'to pull'). The alternate kanji 牽き uses 牽く, a more specific verb for pulling vehicles or animals.