Some work permits have conditions prohibiting enrolment in a school or vocational training. Generally, you don't need a study permit if a course is less than 6 months but I'm not sure in your case. Check CIC's website for the exact language and with the call centre.
The OWP does specify right on it that unless authorized hubby is prohibited from attending any educational institution and taking any academic, professional or vocational training courses.....so I think my question is answered lol