When a plant is put into the ground in fall, it may be facing the cold above ground,
but over most of the country, root growth below ground goes right on until the deep soil temperature drops below 5 degrees C. (In parts of the U. S., it never falls that low, and even in the coldest areas, the roots have several months to grow before the temperature underground drops to that point.)
So the comparison is simple. If you plant a shrub in spring, it must acclimate itself to its new home and begin growing immediately. At the same time, it has to produce leaves, flowers, and then endure the rapidly arriving summer heat. Plant the same shrub in fall, and here’s what happens. It becomes happily dormant above ground soon after planting, but the roots have several months to grow and become comfortable and strong in their new home. Then when spring does arrive, the plant’s established and ready to put out strong leaves, new top growth, and lots of flowers. So the difference is obvious: Fall planting gives your plant’s roots a wonderful “head start” over spring planting.