eisig
icy
Extremely cold, similar to ice. Refers to very low temperatures of air, wind, or water.
Trotz der dicken Jacke spürte sie den eisigen Wind im Gesicht.
Despite the thick jacket, she felt the icy wind on her face.

icy
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icy
Extremely cold, similar to ice. Refers to very low temperatures of air, wind, or water.
Trotz der dicken Jacke spürte sie den eisigen Wind im Gesicht.
Despite the thick jacket, she felt the icy wind on her face.

The adjective 'eisig' (icy) is derived directly from the noun 'das Eis' (ice). The ending '-ig' means 'like' or 'full of', so literally 'like ice'.
Das Wasser im Bergsee war eisig kalt.
The water in the mountain lake was icy cold.
You can recognize the meaning from the noun that 'eisig' (icy) describes. If it refers to weather or temperature (e.g., wind, cold), the literal meaning is intended. If it refers to human behavior (e.g., look, silence), the figurative, emotional meaning is intended.
Im Januar herrschten eisige Temperaturen.
In January, there were icy temperatures.
In the literal meaning, 'eisig' (icy) is often combined with weather phenomena. Common collocations are 'eisiger Wind' (icy wind), 'eisige Kälte' (icy cold), or 'eisige Temperaturen' (icy temperatures).
Ein eisiger Wind wehte über das offene Feld.
An icy wind blew across the open field.
In the figurative, emotional meaning, 'eisig' (icy) describes an unfriendly atmosphere. Typical phrases are 'eisiges Schweigen' (icy silence), 'ein eisiger Blick' (an icy look), or 'eine eisige Stimme' (an icy voice).
Nach seiner unhöflichen Bemerkung herrschte eisiges Schweigen am Tisch.
After his rude remark, there was icy silence at the table.
hot
'heiß' and 'eisig' are clear opposites when talking about temperatures. 'heiß' describes something with a high temperature, such as tea, air, or a stovetop. 'eisig' describes extreme cold, often with wind, water, or weather. 'kalt' is general, but 'eisig' is stronger and sounds like cold caused by ice. If something is very warm, 'heiß' fits. If something is very cold and unpleasant, 'eisig' fits.

Vor der Reise wehte am Bahnhof ein eisiger Wind.
Before the trip, an icy wind was blowing at the train station.
Am Mittag war der Sand am Strand so heiß, dass wir Schuhe tragen mussten.
At midday, the sand on the beach was so hot that we had to wear shoes.