The premise of the question contains a geographical misconception: Antarctica does have mountain ranges—the Transantarctic Mountains (3,500 km long), the Ellsworth Mountains (home to Vinson Massif, the continent's highest peak at 4,892 m), and others. However, the concept of "distinct biomes" within them doesn't apply in the traditional sense.
In the McMurdo Dry Valleys (Transantarctic Mountains) and similar ice-free zones, you find microhabitats with distinct microbial ecosystems: hypolithic communities under rocks, endolithic microbes inside porous sandstone, and meltwater-fed streams with cyanobacterial mats. These vary by moisture, salinity, and substrate—but they're microbial, not biome-scale.
So while Antarctica has impressive mountains, they don't host biome diversity. The continent is essentially a single, vast polar desert biome (or ice sheet biome), with microscopic life in rare refugia.