What harm does it do to a hay field to graze it after the last cutting. If any.

If you are refering to alafalfa: 1) put out bloatgaurd blocks containing poloxolene to prevent bloat 2) pull cattle when it is extremely wet 3) flash graze if possible so you can put a hoof print on as much of the field possible. According to Dr. Richard Berberette @ Oklahoma State this will reduce alfalfa wevil overwintering survival by 50%. There may some slight crown damage to alfalfa but @ today's feed cost it is worth the gamble in my opinion.