To dream of hay represents a burden, the necessity of hard work, or feelings that something mundane has to be done personally and repeatedly. You may also be feeling that a situation is too boring to endure, or hopelessly unimportant.
Example: A man dreamed of having his mouth completely stuffed with hay. In waking life he feared speaking out about his dislike of a demotion at work because he felt he had to show appreciation for having a job at all by accepting all the boring unimportant hard work and never speaking negatively about it.
*Please See Farm