Btw I'm an engineer for a tire company.
Seems like almost everyone who has commented here has relied on secondary information. They read it on a site somewhere or its "common knowledge." I appreciate that you were posting information in an attempt to answer someones questions but if you don't actually know, or you are referencing some other information you found or saw someone else, at least qualify your response so that people can evaluate it. Even though I'm an engineer I don't assume I know everything there is to know, and when I put out my opinion I make sure its labeled as an opinion.
After posting my comments here, I asked the questions because I was interested to see where everyone is getting their information from. I went digging around the internet and couldn't find much of anything. There really isn't anything anywhere on how winter tires work and why they work. If you do find references to snow driving and tire pressure, go ahead and link them.
Siping is made to trap very small pockets of snow and ice because nothing adheres better to snow and Ice than more snow and Ice. If you question this go make a snowball, and then try to stick it to something else. This goes back to Adhesive vs Mechanical traction.
Rubber has a low heat transfer rate so even though it is in the "freezing snow" the tires are in fact well above the temp of the snow. Tires tend to hold in heat and that is actually one of the biggest considerations in designing tires. Deflection of a tires sidewall is a form of work and creates heat. Tire pressure has a huge effect on tire temperature because if your tires are deflecting more they are doing more work and more heat gets stored in the tire.
The racing car with the narrow tires also has spiked and studded tires. So digging through the snow and getting down to ice and possibly ground is much more effective for them. But we don't have spiked studded tires. If it were a real advantage, we'd all have 4 donut spares on for winter driving.
The 4.7 psi drop is from some engineer getting too picky with the numbers.
The idea is to hold your tires at a constant Volume between Summer and Winter. So basic chem, ideal gas law PV=nRT. To hold the V constant ,n and R are the same so P1/V1=constant and you can set the 2 equal. P1/T1 =P2/T2. Temperature has to be in an absolute temp scale so you have to change degrees Fahrenheit to Rankin. If you are looking at the difference in tire pressure from 10F to 80F. 10F=470R, 80f=520r. P2/35= 470/50. P2=31.6 psi which is a drop of 3.6 psi purely from the temp difference. If you measure from 90F to 0F you get a 4.7 psi drop.
Yes you are right, Tread depth tread width and angle are all important. There are literally thousands of tread designs that give a specific advantage in different situations and are less effective in other circumstances. So to discuss tread design specifics is pretty much impossible. We can just talk in generalities.
And then there are lots of mechanisms that testing is the only way to qualify. Tire design is much less exact and less developed than a lot of other engineering. The amount of testing involved in taking a tire from concept to construction is impressive.