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Cold sores are caused by the herpes virus and while dogs can get the herpes virus this is a different strain of the virus.
The answer is no dogs can not get cold sores from humans nor can they pass them on to other humans.
I hope this has been helpful, please reply back if you have additional questions or concerns.
The Herpes virus is transfered by direct contact with an infected dog.
In dogs this normally effects the reproductive tract while in cats it more commonly causes upper respiratory problems.
Here is some additional information about the herpes virus in dogs