What possible issues with running a fan inside a freezer?
No the motor will not freeze. Dont believe the reduction in temperature will have any major impact on the motors performance curves either. However I don't know how effective the system will be in achieving your desired cooling response. Isn't the refrigeration unit's internal fans taking care of the uneven temperature?

If you would like some detailed reading here is a link. If you are worried about the performance it is best you refer to the motor's datasheet.