It is true that the thinner atmosphere is also colder at elevations, it here’s an example of what you can easily find if you search:
At high altitude trees don’t grow (tree line), but grass and heather does. That is not because of the lower level of Oxygen (H2O), or lower temperature level, as we probably all learn in school, it’s because of the low level of Carbon Dioxide (CO2).
If that were true, the tree lines would be moving up as the overall level of CO2 in the atmosphere increased, and the minimum-required level of CO2 became available at higher altitudes.