Can a person catch a cold from having a fan blow on them when they sleep? I did and I woke up with a sore throat and have started sneezing.?

Not really. But the air can cause your throat and sinuses to dry out AND kick up dust, dander, and other allergans into the air for you to breathe in. These irritants can cause sneezing, watering eyes, and even coughing. If your throat and nasal passages are dried out, it might make it harder to be rid of any floating germs in the air.

Most people already have the "cold virus" in their system.

A condition must occur to "activate" the virus.

I for over forty years have used a fan to assist in sleeping. The cool air to make breathing easier, and the fan noise to create a cover of ambient noises.

I believe it is more likely that you became infected (sore throat and sneezing) from another source.