ODB/ Readiness Driving Procedures

I have 1999 Odessy which failed inspection becuase the the OBD Readness Monitiors were "Not Ready". The mechanic told me to drive the car for about 100 miles or so and come back and he would check again.
Is this correct ? It's below freezing tempatures here in NY will this effect it ? I only have ten days to get it back to the shop. My drive back and forth to work is about 10 miles total. Would this be enough to reset the monitor in a week or so ? There is no information in the manual on this. The battery died right before I had the inspection... which I was told that this was the cause of the monitors to reset.

Driving habeits and lenght of drive does play a part in the OBD going through its checks. 10 miles a day may not be enough to meat the criteria for the system to run a check. Why not just take it out for a lenghty drive a couple of time.