Because the body adjusts it's temperature by radiating heat from the extremities - the arms, legs, and head. So they will not necessarily be an accurate indicator of the child's true temperature. In a very unwell child, their blood pressure will fall; to try and keep the body working, the blood flow is pooled in ther internal organs and the brain; so the outer layers of skin will feel quite cold, even though the child has a temperature.

And as someone pointed out, if it is a hot or cold day outside, the extremities will also be hot or cold accordingly.