The engine may be difficult to start in extremely cold weather (-20F) after a short trip. This can be caused by sticking main relay points.
Car Problem Reports
Mazda Mazda3 Difficult to Start in Extremely Cold Weather
Mazda Mazda3 Problem
Average Mileage: 69,266 mi (61,000 mi - 81,800 mi)
Visitor, 2006 Mazda Mazda3, 65,000 mi
During extremely cold weather, the car would not start. After knocking on the starter, it would finally go. This happened for 2 winters. I was going to replace the starter on the 2nd winter, but I could not get one anywhere. The fix was I moved away from Chicago to Denver. Havent had that problem for 2 winters since
Visitor, 2005 Mazda Mazda3, 81,800 mi
The engine is very difficult or has a VERY hard start in the cold weather after sitting for a number of hours.