Is it better to leave the fan set to auto or always on, especially during extreme cold conditions when furnace is kicking on much more often? The furnace is 3 years old.

It won't change the cycle rate of your furnace unless it adds to the overall heat loss of you home. Also see here (https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html#post268203).

Thank you. I can see what you mean, but I guess what I was asking is "is it better or more efficient to leave the fan on and/or less strain on the fan due to not having it go off and back on so much?