TL;DR
Through winter, a daily vitamin D supplement supports normal immune function when sunlight is scarce. Zinc may shorten a cold slightly if started early, but sleep, hydration and hand hygiene matter most.
Short winter days mean less sunlight on the skin, and that means many people make less vitamin D. Vitamin D supports normal immune function, so a daily supplement through the darker months is sensible for most adults and is widely recommended by public-health bodies.
Zinc is often mentioned for colds. The evidence suggests it can shorten a cold slightly, but only if you start it within about a day of symptoms appearing, and it will not stop you catching one. Vitamin C is popular, but for most people it does not prevent colds; it is safe in normal doses and no more.
None of these replace the basics. Good sleep, staying hydrated, a varied diet and regular hand-washing protect you more than any single pill. If symptoms are severe or persistent, or you are pregnant or taking other medicines, check with a pharmacist before starting a supplement.
This article is for general information and is not a substitute for personal medical advice. Always read the label and speak to a pharmacist or doctor if you are unsure.