Milky or cloudy water is often caused by oxygen bubbles in the pipes that are released when the water leaves the tap. Cloudiness and air bubbles do not present a health risk. During colder months, water in outdoor pipes is colder and holds more oxygen than household pipes. Consequently, when the cold water enters your building and begins to warm, the oxygen bubbles escape and cause the water to look cloudy or milky. Construction in the distribution system can also allow air to enter the pipes and cause the appearance of cloudy water. Hot water can sometimes be cloudy due to dissolved gases in the water escaping as the water is heated. Cloudiness and air bubbles should naturally disappear in a few minutes.
You can test this by running the cold water into a clear container and observing it for a few minutes. If the water clears from the bottom to the top of the container, air bubbles are rising to the surface. If the water in the glass clears from the top-down, and white or grey particles settle to the bottom, this may indicate a water heater issue.