Do snow leopards have predators? The answer is a clear, No, with one notable exception: the human.
The reason is a common sense one: there are no predators as able as the snow leopard over much of its range. Apart from humans the snow leopard’s only competitors are wolves. I can’t confirm if the distribution of Bengal tigers in the hills of Bhutan overlaps with the snow leopard. I don’t think it does.
At the lower levels of the Himalayas the range of the snow leopard overlaps with the common leopard but they appear to live harmoniously.
There is nothing in the literature that I have or in my mind which suggests that snow leopard cubs are preyed upon by other predators.
The ‘threats’ to the snow leopard’s existence are (1) loss of prey due to hunting by people (2) degradation of habitat by people and livestock (3) retaliatory killings by farmers (4) poaching (5) climate change (6) mining – loss of habitat (7) building of infrastructure (8) roads and railways. These are all human generated.
The worst poaching and illegal trade takes place in China.
The IUCN Red List has recently decided that the snow leopard is less endangered than they once believed and reclassified the animal as Vulnerable rather than Endangered. Conspiracy theorist claim this is due to pressure from the trophy hunting lobby. In my opinion it was a mistake and, personally, I don’t trust the IUCN Red List.
There is nothing more to say in answer to the question in the title.