The only relevant verse here is in 1 Corinthians:
Does not nature itself teach you that if a man wears long hair it is a disgrace for him . . . (1 Corinthians 11:14)
In first century Greece, long hair identified a man as a homosexual.
For example, in Juvenal’s Satires (8.112-131) he refers to a “long-haired catamite” in Corinth. So I think the hair-length here is based on the cultural implications and expectations. Some interesting and relevant discussion on sexual identity in Corinth is given in Sexual identity in Corinth
I tend to think the principles are still relevant, but the specific practices are probably based on local culture. Therefore, it depends on how long hair for men is seen in the culture in which you live. For example, in some parts of India, long hair identifies you with particular Hindu religious groups and is therefore best avoided for Christians. In our own western culture, long hair is not seen as an indication of your sexuality or religious beliefs, so this verse does not provide a compelling reason for Christian men to avoid long hair. On the other hand, it does suggest that we should avoid behaviours that are commonly associated with immorality.