I agree with some of the comments above - it does depend on the industry and the specific employer.
However, I gather it's still difficult to find a job nowadays. No sense making an already difficult task even more difficult. I think your odds will be better with short hair, styled conventionally and conservatively, as part of an overall well-groomed presentation.
Many of my professional colleagues and business clients still pass comments about and make assumptions based upon appearances. It's shocking, really.
Good luck with the job search, old sport.