In your sentence
A snowball strategy occurred as administrators were asked to refer special education and general education teachers.
means nominating or mentioning someone for inclusion.
I referred a friend to the club for membership.
The "snowball strategy" in your example is
snowball sampling a non-probability sampling technique where existing study subjects recruit future subjects from among their acquaintances.
The administrators were asked to suggest teachers to be included. One of the main problems with this technique is
since the administrators are playing a curatorial role.