Step 1: Put the clues together.
The child has cold feet needing warm socks even in summer, high blood pressure, a femoral pulse weaker than the radial and carotid pulse (radiofemoral delay), and rib notching on chest X-ray. This combination is a classic textbook picture.
Step 2: Explain each clue with coarctation of the aorta.
Coarctation is a narrowing of the aorta, most often just after the origin of the left subclavian artery, near the site of the ductus arteriosus. Blood flow to the upper body (arms, head) is normal or increased, giving strong radial and carotid pulses and high blood pressure in the arms, while flow to the lower body is reduced, giving weak, delayed femoral pulses and cold legs and feet, hence the warm socks. To bypass the narrowing, blood flows through enlarged collateral vessels, including the intercostal arteries, and these dilated, tortuous vessels erode the underside of the ribs over years, producing the notching seen on X-ray, usually from the third to the eighth rib.
Step 3: Rule out the other options.
Femoral artery thrombosis would cause an acutely cold, pale, pulseless leg, not high blood pressure or rib notching, and would not explain years of cold feet in a young child. Raynaud's disease causes episodic colour change in the fingers with cold exposure, not a blood pressure difference between limbs or rib notching. Takayasu's arteritis, "pulseless disease", can cause weak pulses and hypertension, but it is an inflammatory, vasculitic disease of the aortic arch and its branches, and this exact triad, especially rib notching from enlarged collateral vessels, is specifically tied to coarctation, not to Takayasu's.
Step 4: Final conclusion.
The full picture, radiofemoral delay, upper limb hypertension, cold lower limbs, and rib notching, points to coarctation of the aorta.
\[ \boxed{\text{Coarctation of aorta}} \]