Back in the mid-1700s, tobacco developed a strong following among doctors, possibly because Indians used the stuff to treat a variety of illnesses, and they were just riffing off that. By the late 1700s, they had arrived at the conclusion that tobacco enemas were just the ticket for reviving drowning victims, and it was considered that the most effective means of treatment – which would at once warm and dry the innards of the unfortunate – involved blowing tobacco smoke up their arses. The nicotine was also thought to stimulate the heart, thus aiding in the process of resuscitation. In Britain, they actually established stations along heavily used waters which were equipped with all of the necessary tools to safely effect smoke-blowing. These included, among other things, a small bellows, a small fumigator in which to set the tobacco aflame, along with metal tubes to be inserted into the orifice.
So now we know where the phrase “blowing smoke” originated.