It gets really cold around dawn.

Literal

Dawn near [topic-は], sharply cold-become.

明け方 ('dawn, daybreak') is a set noun — literally 'bright-direction,' the moment when the sky starts brightening. 近く ('near') here functions temporally: 'around/near dawn.' ぐっと is a mimetic adverb for 'sharply, with a pull, markedly' — here intensifying the cooling. 冷え込む is a compound verb for 'to grow chilly / cool down sharply,' stronger than plain 冷える.