Vitamin D is unusual among nutrients because most of it is manufactured in skin rather than eaten. That manufacture depends on conditions that fail entirely for part of the year in many places.
The reaction needs a specific wavelength
Ultraviolet B light converts a cholesterol derivative in skin into a precursor of vitamin D. Only a narrow band of ultraviolet wavelengths drives this reaction.
That band is filtered out heavily when sunlight passes through the atmosphere at a shallow angle. The relevant variable is the sun's height in the sky rather than brightness or warmth.
A bright cold winter day at high latitude can therefore produce no vitamin D at all, while a hazy summer day produces plenty. Perceived sunshine is a poor guide.
Latitude and season set the availability
Above roughly the latitudes of northern Europe and the northern United States, the sun sits too low through the winter months for meaningful synthesis.
The period during which synthesis is possible narrows with increasing latitude. Nearer the equator it continues year-round, which is why guidance differs so much by country.
Time of day matters for the same reason. Synthesis is concentrated in the middle of the day, when the sun is highest, and drops away sharply toward morning and evening.
Skin, clothing and glass all intervene
Melanin absorbs ultraviolet light, so more heavily pigmented skin requires longer exposure to produce the same amount. This is a straightforward optical effect.
Ordinary window glass blocks the relevant wavelengths almost completely, so time spent in a sunny room contributes nothing. Sunscreen and clothing also reduce synthesis by design.
These factors combine, which is why two children in the same city can have very different status from apparently similar routines.
Dietary sources are limited
Few foods contain appreciable vitamin D naturally. Oily fish, egg yolk and liver are the main ones, and none is eaten in large quantities by most young children.
Fortification of products such as spreads, cereals and some milks exists partly to address this, and which products are fortified varies considerably by country.
Because dietary supply is small and synthesis is seasonal, stores built in summer are drawn on through winter. The status a child reaches by spring reflects both.
Why children are treated as a distinct group
Vitamin D is involved in calcium handling and bone mineralisation, which matters most during periods of rapid skeletal growth.
Infants have very small stores at birth, which is why many countries issue specific guidance for the first years and for pregnancy.
Whether a supplement is appropriate, and in what form, depends on age, diet, feeding method and local guidance, and it is a question for a health visitor, pharmacist or doctor rather than one to resolve from general reading.