The hut on Snowdon - please NEVER use "mount"! is the Halfway House, a very welcome caff /teastop on the interminable Llanberis route.
British hills rarely use mount - if they do they are usually undulating moorland hills in Eastern Scotland , where the word is variant of Mounth or Monadh - an elevated plateau or area of high grazing.
It is a bit of Victorian exageration, copying Latin I expect, but it grates with most hill goers.