。
I caught a cold from being exposed to the night mist.
Literal
Night-mist [to-に] exposed-[and-て] cold [obj-を] pulled.
~に当たる has several senses; here it means 'be exposed to, be hit by' (rain, wind, sun, mist). 風邪をひく ('catch a cold,' lit. 'pull a cold') is a fixed collocation — one of many set expressions using ひく ('pull, draw') for abstract things. 夜霧 is a compound for 'night mist, evening fog' with a poetic feel.