Quick answer = Yes
Significant changes in altitude affects tire pressures when traveling from one elevation to another. Fortunately, this influence is relatively small and can be easily accommodated.
Atmospheric pressure is the force exerted on objects by the weight of the air molecules above them. While air molecules are invisible, they have mass and occupy space.
However, as altitude increases, atmospheric pressure decreases. For example, atmospheric pressure pushes against the earth at 14.7 pounds per square inch (1 kilogram per square centimeter) at sea level, yet drops to only 10.1 pounds per square inch at 10,000 feet as indicated in the following chart.
When it comes to measuring tire inflation pressure, it is important to realize there is a difference between atmospheric pressure and gauge pressure. Most pressure gauges (including all tire pressure gauges) are designed to measure the amount of pressure above the ambient atmospheric pressure.
Imagine removing the core from a tire valve and allowing the air to escape. Even after the air has completely stopped rushing out of the valve, the tire is still experiencing 14.7 pounds per square inch of atmospheric pressure. However, a tire pressure gauge would read zero pounds per square inch of tire inflation pressure because the pressure outside the tire is equal to the pressure inside.
Since a tire mounted on a wheel essentially establishes a flexible airtight (at least in the short term) pressure chamber in which the tire is shaped and reinforced by internal cords, it retains the same volume of air molecules regardless of its elevation above sea level. However, if tire inflation were set with a tire pressure gauge at sea level (where the atmospheric pressure of 14.7 pounds per square inch is used as ambient atmospheric pressure by the gauge), the same tire pressure gauge would indicate the pressure has increased at higher elevations where the ambient atmospheric pressure is lower. Those measured at the 5,000-foot level (where an atmospheric pressure of only 12.2 pounds per square inch is the ambient pressure) would indicate about 2-3 psi higher than at sea level. On the other hand, traveling from a high altitude location to sea level would result in an apparent loss of pressure of about 2-3 psi.
However, the differences indicated above assume that the tire pressures are measured at the same ambient temperatures. Since tire pressures change about 1 psi for every 10° Fahrenheit change in ambient temperature, the tire pressure measured in the relatively moderate climate typically experienced at sea level will change when exposed to the colder temperatures associated with higher elevations.
This means that in many cases differences in ambient temperature may come close to offsetting the differences due to the change in altitude. Depending on the length of their stay at different altitudes, drivers may want to simply set their cold tire pressures the morning after arriving at their destination, as well as reset them the morning after they return home.