Step 1: Understanding the Concept:
In an oil-in-water (O/W) emulsion, oil droplets are dispersed in water. In a water-in-oil (W/O) emulsion, water droplets are dispersed in oil.
Step 2: Check each:
Milk: fat droplets in water, O/W. Vanishing cream: O/W (it feels non-greasy). Paint: a dispersion of pigment, not a W/O emulsion.
Butter: tiny water droplets dispersed in fat, so it is W/O.
Final Answer:
Butter is a water-in-oil emulsion, option (D).
\[ \boxed{\text{Butter}} \]