What are an employees rights regarding their religious customs and a company dress code?

There is no definitive answer: it depends on circumstances. Employees and prospective employees have had success in forcing modifications of dress codes (or other rules--like whether you work on Friday night, Saturday, or Sunday) based on religion: for example, male Orthodox Jews would be allowed to wear yamulkes even in situations when hats are not otherwise allowed; female muslims have won the right to wear their coverings.

There are two main issues:

1) The dress code infraction in question must be mandated by the religion itself, and not merely be customary among its followers. For example, say that most members of a certain protestant church had themselves tatooed with a picture of Jesus. If such a tatoo was not actually required by their faith, but was simply custom at their church, their likely would be no protection for it.

2) There must be a way for the dress code infraction to be safely accomodatated. For example, I have never seen a religious muslim woman as a lifeguard at a public pool or beach--there is no way to safely reconcile the dress code with the need to dive into the water without warning or delay.

In your case--and not knowing anything about your faith, this may be an ignorant question; if so, I apologize--if the long hair is simply a custom and not a religious commandment, you probably cannot fight a requirement for short hair. Or even if it is a religious requirement, if it would pose serious issues on the job--e.g. it could get caught in brambles or branches, could be potentially snagged by a wild animal, etc.--then it may still be the case that you could be required to cut it.