I've seen them mounted outside. Some forget filter and simply dump the dust into a box mounted on the outside wall. That does mess with the inside air temperature, the reason I filter the air well and return it to the shop. (My shop has heat and air). My Dylos particle counter indicates it quite efficient. The air in the closet, after the filter, goes through a carefully designed baffle system between the roof trusses to minimize noise from that path.
I've even see installations designed to switch all the air past the cyclone directly outside when the temperature wasn't extreme, and run it through the inside filter otherwise.
My 5hp cyclone is SO loud if it were outside instead of in a sound-insulated closet I suspect the neighbors across the way would be less than pleased. Maybe something to consider.
JKJ