How to implement an enumerated field using hook_schema()? I need to have a field in my database that is shall hold a limited set of enumerated values.

The MySQL ENUM type is not one of the predefined Drupal data types.

So how do one implement a field to hold enumerated values using hook_schema?

I understand that I can do it with a tiny int, but how do I map from and to the strings of enumerated values (e.g. "zero", "one", "two", "three") to integers stored in the DB?
If you are using the Form API to accept this data, you can map integers to string values.

You can also store that mapping array in your .module file.