There is some evidence that it does. A meta-analysis of three high-dose zinc trials found the following:
Zinc acetate lozenges shortened the duration of
• nasal discharge by 34%
• nasal congestion by 37%
• sneezing by 22%
• scratchy throat by 33%
• sore throat by 18%
• cough by 46%
• Zinc lozenges shortened the duration of muscle ache by 54%, but there was no difference in the duration of headache and fever.
The absolute length of these effects is on the order of 1-3 days, so these results are meaningful to most cold sufferers.
The trials were double-blind placebo-controlled, meaning that neither the patient nor the physician knew whether they were getting zinc or a placebo, reducing the chance that positive results were influenced by expectations. Two of the three trials started treatment within 24 hours of symptoms, while the third did not specify a time frame.
The doses of zinc were 80-92 mg/day, about 10 times the recommended dietary intake. The only adverse event reported at these doses was bad taste.
Three trials are not enough to “prove” that zinc is effective, but enough to say that it is more likely than not. Given the lack of side effects, using zinc seems like a sensible way to treat colds.