Currently, GoToWebinar does not have a common chat area. Attendees can text a question or comment, but those go to only the webinar organizer, who can choose individually to forward each message to the full audience.
GoToMeeting does have a common chat where all attendees can see each other's comments.
Adding this feature to GoToWebinar has been mentioned several times here. Some would like to have the option to share the question panel (chat) with the attendees, and some like it the way it is.