Not trying to be rude, but I actually have to disagree with bobharly, although his math and theory are absolutely sound, they apply to objects that are solid, not made of pliable rubber. Now I'm not an engineer or anything but i have been autocross and road racing for a while, and used to be a drag racer before that.
Tires are contructed in a way with different "stiffness" in different areas. Steel belted radials (all street tires now) are designed to be softer in the sidewall than in the tread areas. This is why when you add a few pounds of air pressure,you can see the tire get taller, however, if you were to measure the contact area between a tire at 33psi and then the same one at 35psi, you would need some very high quality equipment to measure the difference, less than 2%. What happens in the real world is that when a tire's sidewall rolls over, you actually have an effect of "jacking up" the inside of the tire. What I mean is that because the tire is designed to try and keep itself flat across the tread(from inside to outside),when the sidewall rolls it is lifting the inside of the tread up, actually removing up to 1/3 of the contact patch from the road. This is why we always raise tire pressures up to around 38-40 psi for racing. So you lose a tiny bit of contact front to back but gain so much in the left to right, when cornoring. Keep in mind that at these pressures, we are also driving the cars quite hard and will add alot of heat, still blowouts are almost unheard of.
Next something different happens when you accelerate or brake;there is weight transfer to the front or rear of the vehicle. When you brake, you are increasing the pressure on the front tires by 2-3 times over that of static. Extra weight causes the tires to squish down and you gain your contact patch back,plus more. Same thing on the rear tires when you accelerate, and this still happens,less drastically,at light brake and throttle applications.
So yes, you technically should lose grip when adding pressure,but in the real world, things happen differently than on paper.
Some other things to remember: we are talking about differences in pressure of 2-4 psi (for street use), not the 20-25psi difference like in racing or off-road environments. Your typical racing slick for drag racing is NOT a radial,it is a much softer bias-ply, designed that way for absolute maximum traction in a straight line, and run at about 15psi. Off-road tires are designed to be aired down to around 6-9psi, from the typical 30-35psi they would use on the street. If you were to run 15 psi or less in your street tire, your chances of doing damage to the tire from overheating go up drastically. You can't compare the two for the prupose of saying that you should or shouldn't do. The reason you CAN apply that to autocross situations is because we use street radial tires all the time.
Also, snow is different,trust me, i live where snow on the ground is a reality for 5-6 months of the year. Narrow tires to cut through the snow is better,because any contact patch on the ground is better than a big contact patch on snow.
(almost done guys, lol)
So adding 2-3 psi will not put you in danger of blowing out a tire, it generally offers a little better gas mileage, but does affect the ride quality. I would never recommend running a tire at 40+ psi all the time, unless you are a glutton for punishment, lol. You put yourself in more danger by running a tire underinflated than overinflated.