I have a 2005 Mazda Tribute that when the temperature drops cold, it won’t come out of park. The past 2 years now when it gets cold outside I can’t get the button on the shifter pressed in to put it in gear. I have to wait until the car is warm before it breaks lose and only then will it come out of park. Needless to say this is very aggravating. Any ideas on why this is happening?
The problem might be with the transmission shift inter-lock system.
This safety system requires that the brake pedal be depressed before the transmission can be shifted out of park.
This system has a switch at the brake pedal, and a solenoid at the shifter.
That’s what I’d check.
Tester
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That is assuming the OP is applying the brakes before trying to shift it out of PARK. 
OP?
Thank you! I’ll try that
If you are referring to the driver. Yes I do and know that you have to apply the brake when shifting the vehicle out of park and any other gear
Check to see if your brake lights come on when you press on the brake pedal. If they don’t, that can provide a clue to what’s wrong.
My cars have always been manuals, and one time about 15 years ago I rented a car in San Diego for a desert winter holiday. I parked to look at some cactus out in the middle of nowhere, nothing but raw desert in all direction and hadn’t seen another car for hours, and what do you know, when I decided to leave, I couldn’t get the transmission to shift out of P … finally figured it out, but for a while there I was thinking Twilight Zone.
You know you can leave it in neutral, set the parking brake, and start it in neutral the next time you want to drive?
I don’t have a manual transmission, the ONLY time it does this is when it’s cold outside. I have to let the vehicle warm up totally and then and only then will the shifter button will push in, letting me get out of park. This started last winter. Now here’s winter again and it is doing the same thing.
Do your brake lights at the rear of the vehicle come on when you press on the brake pedal and this symptom is happening?
Either the brake-shift interlock solenoid is weak or a sticky beverage was once spilled into the gear shift assembly.