Why do few plants grow in tundra?

It is very cold and the plants cannot survive.

If you want your answer in a Biology view of point, then:

Plants cannot survive in the cold because cold makes the chloroplast in the plant not function correctly, and this is also the reason why leaves of trees turn red and orange during the fall and fall off during the winter.

However, there are some plants that can survive in the cold, like shrubs.