Why are tundra plants usually small?

Short season for growing and cold temperatures.

Tundra biomes are either found at high latitudes or high elevations in mountains. These are both very cold environments that are dominated most of the year by snow and icy conditions. This in itself tends to stunt plant growth.

These regions, especially, tundra in the high latitudes also have very short growing seasons (3 months perhaps) and so plants can only photosynthesize and store sugars for this amount of time. High winds in these environments also tend to keep plants low to the ground.