Hello Its actually not a bad time to visit these two places. It'll be cold but not freezing. If you love being bundled up in warm clothes and seeing hours of fog and dew drops as ice on plants, you'll love Ooty and Kodai in Jan. Otherwise, March, April would be the best time.
It is a good time to visit both the places. It will be cold but not exactly like the cold weather you get in the mountains of north india.I'm attaching with this comment travel guide for both the places, you can go through them and plan your trip.