Final answer:
Ornette Coleman, an innovative alto saxophonist, usually played the woodwind instruments in his own quartet, but without more context, it's challenging to specify the current woodwind player's name in a particular Coleman quartet.
Step-by-step explanation:
The question 'Who plays woodwind in Coleman's quartet?' pertains to a group of musicians and specifically asks about the person responsible for playing the woodwind instruments in that ensemble.
Ornette Coleman, a notable figure in the world of jazz, typically played with a quartet where he himself was the primary woodwind player, as he was an innovative alto saxophonist. In traditional jazz quartets that feature woodwind instruments, the players can range from playing the saxophone, clarinet, flute, or bassoon.
However, without additional context or the specific name of the quartet, it is difficult to provide the name of the current woodwind player in question.