The correct answer is - Tundra is much cooler than deserts, so less water evaporates during the growing season and the tundra stays more moist.
The tundra is a very cold biome. In fact, most of the year is winter, and there is only a short period of time when it is summer, and that is not really a summer in the true sense of the word, as it is relatively cold and fresh.
Since for most of the year the tundra is frozen, the water is not evaporating, and during the very short ''summer'', it defrosts, so it becomes all very marshy, and that allows the plants to grow there.
Also, because the summer so short and relatively cold, the evaporation of the water is minimal, so most of the water just frozen again in the winter.