Why do my tires lose pressure in really cold weather?

During the day when the tires are cold; before you leave work is perfect (assuming you work 8-5). I’m guessing a most mechanics think STP is an engine cleaner, and don’t associate it with standard temperature and pressure. There is no industry standard temp, because the “standard” is whatever temperature the tires are operating at. As long as you’re checking your tires once a month, it shouldn’t be a problem.

Yes.

The reason you got a slightly different answer was that you forgot that the pressure is absolute, and not gauge. 32 psig is 46.7 psia. A pressure drop of 13.6% gives you a pressure of 40.3 psia. 40.3 psia minus 14.7 psia atmospheric pressure is 25.6 psig.

Overinflated tires are safe right up to the max PSI rating. Ride comfort might suffer slightly, but will not be a big deal with the variances discussed here.

Under-inflated tires can be quite dangerous.

When filling your tires, and concerned temps might plummet, go ahead and add a few more PSI. If your recommended tire pressure is 32, going up to 40 is no big deal, and helps ensure you won’t drive on under-inflated tires.

YMMV. Literally.

Generally you are supposed to measure tire temperature when cold, or at least after the vehicle has rested for several hours.

I don’t think this is completely true. Over-inflated tires can interact with your suspension, increasing stopping distances. You may end up bouncing your tires.

On certain hypermiling message boards, posters can be found that routinely run 175% of routine suggested PSI.
Some posters have reported that their car’s handling gets worse. One driver with a small FWD car noted that his car has a serious tendency towards oversteer once he went past 75 PSI.
Another noted that his vehicle’s ability to climb snowy hills decreased dramatically when he goes from 32 PSI to 44 PSI, and then again precipitously as he moves to 55 PSI and 65 PSI.

There’s a poster who has driven over 110K miles with his 55 PSI tires running at 110 PSI, and has apparently neither been killed by it, nor experience excessive tire wear, as he’s still on the factory tires.

[1] Hypermiling defined by Wikipedia:
Hypermiling is a term used in North America that refers to a set of techniques used to maximize fuel economy. Those who practice the techniques are referred to as “hypermilers.” The term was originally coined by Wayne Gerdes, who is considered by the media to be one of the top hypermilers in the world,[1] and is known to hold the record for gas mileage in some common vehicles, including 30 miles per gallon (mpg) in an Acura MDX and 59 mpg in a Honda Accord.[2] In 2008, the word hypermiling was selected as the best new word of the year by New Oxford American Dictionary.[3]