The reason that you need to add air to your tires when it gets cold is because the gaseous oxygen molecules take up less space in the tire because of the cold weather. Charles’s law says that temperature can cause the volume of a gas to expand when it gets hotter, and shrink when it gets colder. Adding more air to the tire adds that volume back to make it full again.
A balloon pops when you put pressure on it because of Boyle’s law. Boyle’s law says that when you reduce the volume of an item, the pressure increases. When you push on a balloon, it puts more pressure on the air in the balloon. This in turn decreases the volume, which puts more pressure on the balloon’s walls. This extra pressure can be too much for the walls and cause it to burst.