From the most recent study from that Wikipedia page, dated 2015 Feb 25:
"Zinc acetate lozenges shortened the duration of nasal discharge by 34% (95% CI: 17% to 51%), nasal congestion by 37% (15% to 58%), sneezing by 22% (1% to 45%), scratchy throat by 33% (8% to 59%), sore throat by 18% (10% to 46%), hoarseness by 43% (3% to 83%), and cough by 46% (28% to 64%). Zinc lozenges shortened the duration of muscle ache by 54% (18% to 89%), but there was no difference in the duration of headache and fever."
"Given that the adverse effects of zinc in the three trials were minor, zinc acetate lozenges releasing zinc ions at doses of about 80mg/day may be a useful treatment for the common cold, started within 24hours, for a time period of less than two weeks."
The Wikipedia summary of this study is horribly worded and one could easily read it as the zinc lozenge having no effect, which is exactly the opposite of the study's conclusion (that zinc does has a positive effect on cold symptoms). The study's purpose was to determine if zinc lozenges only affect/improve symptoms in the pharyngeal region (the throat) since a lozenge is dissolved in the mouth and throat, or if the zinc has an improvement effect in the nasal region as well where it is not directly dissolved. The study showed that zinc *does* improve symptoms in the nasal region. The conclusion that the Wikipedia article is summarizing was that there was no difference in the effect of the zinc treatment depending on anatomical region - the zinc lozenge improved symptoms in both the throat and the nasal region.