In the winter, summer, spring or fall worn tires have the possibility of losing traction. Winter is obvious. Snow-covered roads will cause your vehicle to slip and slide. Every winter we get multiple curb slammers, which is actually a best-case scenario. If you didn't slam that curb what if it would have happened on the freeway at a faster speed? We try not to go there. In the heat of the summer, the asphalt will seep oil into the surface of the road. If it happens to rain this can become extremely dangerous. Water and oil do not mix well and worn tires will not grip.
As you have probably heard if you are driving an all-wheel drive the tires need to be replaced in a set of 4 so that no damage can occur to your transfer case or PTU (power transfer unit). We have actually seen problems arise from 1 or 2 tires getting worn more than the others and cause damage. Your systems have very little tolerance. We have also seen some people that want to take a chance with their very expensive AWD system and only replace 1 or 2 tires that don't match the other 2. In most instances, this doesn't end well. We highly advise always replacing tires in sets of 4 for AWD and at least a set of 2 for other applications.
Don't just install tires but get a wheel alignment service too. One more thing to consider. The shocks and struts are one of the main reasons that your tires get worn and when your shocks and struts are worn even with brand new tires your stopping distance can take longer than it should.