Refer to figures.
When carrying out a steady glide descent, there is no thrust. The forces of lift, weight and drag must therefore be in balance. For a given IAS, we can calculate what the descent angle (γ) is. This is the angle relative to the air. The descent angle through the air is not changed by wind. 

The rate of descent is also not affected by wind.

The glide path angle however, is the angle of our descent relative to the ground and not the air. This is affected by the wind. In a headwind, the magnitude of the glide path angle increases. This decreases the total glide range. The opposite occurs in a tailwind, which decreases the size of the glide path angle and increases glide range.

Note: The absolute glide path angle technically decreases in a headwind. For example, if it was -3.0° it may decrease to -4.0° in a strong headwind. However, the “magnitude” (the value without considering the minus sign) has increased.