According to the Alpenzoo at Innsbruck, Switzerland, alpine plants are specifically suited to the high, cold, rocky environments they originate from. Because they are low growing, they stay out of sometimes bitter winds. They also require fewer nutrients, a factor which also may contribute to their small leaf size. They have tap roots which reach through rocks to the soil.
There are many varieties of alpine plants that require acid soil as is found around limestone or pine needles in the mountains. Both limestone as a rock garden and pine needs as a soil amendment can be used, but check before planting as levels of acid requirement vary by plant. Some acid loving alpines include Arethusa, Creeping Snowberry, Twinflower and Wintergreen.
The website Plant Ideas lists dozens of alpine plants that don't need any special chemical composition in the soil and grow well in garden loam. Drainage is still important for these plants. These plants bloom at different seasons and cover the color spectrum including Wooly Yarrow, Colorado Columbine, Japanese Hardy Aster and Mountain Bluet.
Some alpine plants are accustomed to dry, sandy environments. Plant them in sand, loam and humus -- and sphagnum in dry climates, make sure they can drain and give them full sunshine and they should thrive. These include Silver Alpine Yarrow, Crested Iris and Sea Campion.