The Scottish SPCA was alerted to the incident in Gorebridge after a member of the public discovered the dog, believed to be a cream and tan saluki, on top of the 6ft hedge bordering their property on Tuesday.
The dog also had its fur shaved off, leaving him at the mercy of snow and freezing temperatures.
Scottish SPCA Inspector, Fiona Thorburn, said: “This was an extremely callous act and the dog is incredibly lucky that he was spotted.
Edinburgh crime: Man critical after suffering serious head injury in city centre ‘fight’
Edinburgh weather: Capital and the Lothians warned as Met Office predict thunderstorms to follow heat wave
West Lothian fire: Pictures show firefighters still battling West Lothian wildfire which broke out three days ago
Lothian bus driver ‘hit by stone’ as police launch witness appeal
Sharleen Spiteri: Texas singer rescues young bird while playing East Lothian music festival
“Salukis are thin dogs who feel the cold anyway but without any fur for protection, it’s likely he would have succumbed to the elements within a day or so if he hadn’t been found.
“The dog is a young male who is not neutered and who we believe is cream and tan in colour.
“We believe he may have been shaved in an attempt to disguise his breed as salukis are quite distinctive looking dogs.
“He has been taken to one of our animal rescue and rehoming centres where he is receiving lots of care and a warm bed.
“We would like to find out what happened to the dog. If anyone recognises him or has any information on how he came to be in this situation they can contact our confidential animal helpline on 03000 999 999.”
It comes after a dog found by a roadside in Dunfermline late last Friday was found to have been shot in the head.