This is the 2568th most frequent Japanese word.
寒く
"Cold" (adjective).
寒く (samuku) functions as an adverb in this sentence, describing the extent to which it feels cold.
今日はとても寒く感じます。
Today, it feels very cold.
寒く (samuku) here describes the temperature or the ambiance, adding to the imagery of a quiet, cold sky.
空が寒く静かです。
The sky is quietly cold.
寒く (samuku) is used as part of a compound sentence to indicate the cause ('cold') that leads to the result ('hands are numb').