We often see lot of pictures of Lord Shiva sitting in the snow clad mountain of Kailasa.
Does it represent anything symbolically?
P.S. I'm not interested in the story of how Shiva came to live on Mount Kailasa.
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Lord Shiva is symbolically represented as dwelling in Mount Kailash because he is said to be too iridescent, vivacious and fiery. The mountain's cool and serene environment and the goddess Ganga on his matted locks atone for his fiery nature. (Although Goddess Ganga flows from his locks for an another reason). Being the supreme lord, he is ever absorbed in meditation on himself to regulate the cosmos.
The symbolic meaning behind Kailasa is that it represents celebration. Also, it is interesting to note that Shiva also said to reside in the Smashana:
The abode of Shiva is in Mount Kailasa, and the smashana (the cremation ground). Kailasa means 'where there is only celebration', and smashana is where there is only void. The Divinity dwells in the void as well as in celebration. And in you there is void, in you there is celebration.
An explanation from an article by Sri Sri Ravi Shankar: