▲没错，by moonlight 不用冠词。如：

The castle looks fantastic by moonlight. 城堡在月光下看起来棒极了。

We walked through the palace gardens by moonlight. 我们借着月光穿过御花园。

▲而by the light of the moon则要用冠词，主要是因为 light 受到了后置定语的修饰。类似的表达如 by the light of the fire (the candle, the lamp, torch, etc)。如：

She could just see by the light of the candle. 她藉着烛光勉强能看见。

We sat and talked by the light of the fire. 我们坐在火边，借着火光交谈。

In the evenings we eat by the light of an oil lamp. 晚上我们便在一盏油灯下吃饭。

The house could be clearly seen by the light of the moon. 月光下，那所房子清晰可见。

They sat reading by the light of a 40-watt bulb. 他们坐着，借着一只40瓦灯泡发出的光读书。

We struggled to read the map by the light of the torch. 我们藉着手电筒的光费力地看地图。