To be in a fog or to be in a haze

Fig. confused, not alert; dazed; not paying attention to what is going on around one

To be lost in the mists of time

Fig. to be forgotten because it happened a long time ago

To mist over or to mist up

Fig. to fog up; to develop a coating of water vapor so that one cannot see

To see the red mist

Fig. to lose temper or self-control completely

Scotch mist

Fig. something hard to find or non-existing; something imagined

To have one’s head in the clouds

Fig. to daydream; to be unaware of what is going on from fantasies

Every cloud has a silver lining

Prov. You can derive some benefit from every bad thing that happens to you

To be under a cloud

Fig. to be suspected of something

A cloud on the horizon

Fig. a problem or difficulty which you expect to happen in the future

To live in cloud-cuckoo land

Fig. to believe that things you want will happen, when really they are impossible

To be on cloud nine

Fig. to be very happy

霞 【かすみ】 kasumi, (spring) mist [frequently translated as 'haze']

朝霞 【あさがすみ】 asagasumi, morning mist
夕霞 【ゆうがすみ】 yūgasumi, evening mist
遠霞 【とおがすみ】 tōgasumi, distant mist

This refers to being unable to see things in the distance because they are obscured by a somewhat cloudy atmosphere. This is not a meteorologist’s technical term, but indicates mist made up of fine droplets of water floating in the air. The phenomenon is common in autumn, with ‘fog’ (霧【きり】 kiri) being the established autumn kidai; ‘mist’ (霞【かすみ】 kasumi), is the term for spring. It seems that water vapor rising in warm air, making all of nature look blurred and calm, permeates things with the tranquillity of spring.
In addition to ‘morning mist’, ‘evening mist’, and ‘distant mist’, poets use such phrases as ‘the grass is misty’ (草霞む【くさかすむ】 kusa kasumu) and ‘the bell is mist-muffled’ (鐘霞む【かねかすむ】 kane kasumu). However, when the same phenomenon occurs at night, it is called ‘misty’ (朧【おぼろ】 oboro).

霧 【きり】 kiri, autumn mist / fog

狭霧 【さぎり】 sagiri, thin fog / thin autumn mist
霧襖 【きりふすま】 kirifusuma（きりぶすま）, wall of fog/mist [literally 'fog fusuma', sliding door of fog]

From Bashō:

kirishigure / fuji o minu hi zo / omoshiroki

in the misty rain
Mount Fuji is veiled all day —
how intriguing!