Why will a tire sometimes bump during the winter as a car is moving, only to smooth out its ride after the car has been traveling for a distance?
Quick answer: The tire warms up as the car travels.
Tires are made of long rubber molecules. They attract each other by van der Waals forces.
As your tires sit there with the weight of a 1500 kg car pressing down on them, the molecules slowly slide past each other. The tire deforms, and flat spots appear.
When the temperature drops, the rubber molecules do not have enough kinetic energy to overcome the attractive forces. They cannot slide past each other quickly. The flat spots remain, and the tires bump as you drive along.
The tires are not completely rigid. They can flex a little as you drive along. The friction with the road and the sliding of the molecules past each other generates frictional heat. More molecules can then overcome the attractive forces.
As the tires heat up, the molecules can move past each other more quickly. After about 15 min, the tires may become soft enough so that the flat spot disappears, and so does the thump.
"Flat spotting" is more of a problem with high-performance tires. They are made of softer but stiffer rubber to make more contact with the ground, so they form bigger flat spots.