The effect of zinc treatments on the severity or duration of cold symptoms is controversial. ... Recent research suggests that the effect of zinc may be influenced by the ability of the specific supplement formula to deliver zinc ions to the oral mucosa. Additional research is needed to determine whether zinc compounds have any effect on the common cold.
    - "Zinc and the common cold"

There are conflicting results ... A recent study found no significant differences between zinc nasal spray and placebo. Negative results may be caused by using doses of zinc that are too low or they may be affected by the presence of compounds like citric or tartaric acid, which may reduce efficacy due to chelating of the zinc ion.
    - "Zinc"

... It’s believed that if there is any benefit in taking zinc or zinc lozenges, it is very minor.

Due to this risk of a loss of smell, many experts recommend that you avoid zinc nasal sprays completely.

Zinc’s side effects may outweigh any potential benefit and the benefit may be minimal at best.
    - "Zinc for Colds: Lozenges & Nasal Sprays"

The cold-fighting reputation of zinc has had its ups and downs. That's because many zinc studies — both those that find the mineral beneficial and those that do not — are flawed.

The highest quality randomized trials generally show no benefit. In studies with positive results, zinc seemed most effective taken as a lozenge or nasal spray in the form of zinc acetate within 48 hours of the onset of symptoms. Taking zinc with food may reduce side effects, including a bad taste and nausea. Intranasal zinc may result in permanent damage to the sense of smell.
    - "Zinc"

[Regarding sprays versus lozenges,] "I think it's a matter of personal preference. I've tried both and think that people could probably consider one of them to shorten the length of a cold.

"But theoretically, a spray might be better because colds originate in the nose and eyes, so if you take action at the point of entry, I would think that might be an advantage."
    - Dr. Sherif B. Mossad, "Zinc Spray Shortens Colds"

Therapy with zinc gluconate glycine lozenges significantly reduced cold duration and antibiotic use in school-aged subjects. Prophylactic administration [using a device such as a sprayer] also significantly decreased cold frequency.
    - "Effectiveness of zinc gluconate glycine lozenges"