Here seems to be the correct answer:
http://www.immigration.com/faq/fvisa.html#91
Q45 My wife is here on H4 visa. Is she allowed for the study on H4 or we need to get Student visa for study.
A45 She can study on H-4. But she can not get assistantships or work authorizations that may be available to F-1/J-1 students.