Option 1: Silver is a noble metal and is not reactive with water, therefore it does not produce hydrogen gas with cold water.

Option 2: Sodium is an alkali metal that is highly reactive with water. When sodium reacts with cold water, it produces hydrogen gas. This is the correct answer.

Option 3: Copper is a transition metal and is not reactive with water, thus it does not produce hydrogen gas with cold water.

Option 4: Iron is a transition metal and is not reactive with cold water, so it does not produce hydrogen gas.

In summary, the correct answer is option 2, sodium.