ICE has caused disruption to travel and schools this morning.
Wakefield Pathways School, in Castleford, is closed all day because of the conditions.
The A1(M) is closed northbound between junction 42 and 43 because of recovery work following an accident and a jackknifed lorry.
It is also closed southbound between junction 46 and 45 following a separate accident involving two lorries and a car.
There are also delays because of fog and reduced visibility on the M62 between junction 22 and 32.
Wakefield Council said it was aiming to complete all household bin rounds today, though refuse trucks were moving slowly and with caution.
It said gritters were prioritising main routes and would then move onto bin routes and side roads.
Highways network manager Graham West said: “We urge both drivers and pedestrians to take great care when moving about.
“Black ice forms when supercooled rain falls on to sub-zero temperature roads, washes off the salt and then immediately freezes. This is an exceptional weather condition and we can simply do nothing before the event.
“We gritted last night at 7pm and went out again this morning at 5:30am. Nevertheless, the conditions on both roads and pavements were extremely difficult this morning.”
Temperatures are expected to increase as the day goes on, and weekend temperatures will reach 8 degrees.