Grace's advice is incorrect. You are SUPPOSED to check and inflate your tires to the recommended pressure when the tires are cold. Yes, cold weather does reduce the air pressure of your tire. Generally you lose about 1 PSI for every ten degrees or so (Fahrenheit). Yes driving does also warm up the tires in the winter, but it does in the summer too (even more due to the higher ambient temperatures). Listening to Grace is going to result in a better chance of you needing that spare.
Again ALWAYS check tire pressure when the vehicle has been parked for at least a couple hours to ensure they are "cold". In this case "cold' refers to whatever the ambient air temperature is. Then fill them to whatever the manufacturer says in the owner's manual (or the sticker in the door jamb). Do not refrain from filling them just because it's cold and driving will 'reinflate' them. It doesn't work that way.
Inflate your tire to whatever the manufacturer recommends (assuming you are using the proper tire size) at whatever temperature it is outside. Make sure the car has been sitting for at least a couple hours (preferably without the sun baking the rubber). Any time you see that the pressure is low, you should fill it. Regardless of it being low due to weather or other factors. When you drive, the pressure will go up a bit, but that has all been factored in to the pressure recommendations from the car's manufacturers.
Yes it can happen so be careful about putting more air in it..it might just go down 10psi. Just like during the summer the air pressure can rise in the tires due to the heat.
yes. but once you start driving awhile the air in the tire warms so it expands again. so don't fill your tires up until you are sure it's a leak and not just cold. other wise you're going to need a spare.
Yes the air particals get cold,moveless,fillless space
Yes it's 1psi for every 10°F
