Bear Scotland, which looks after roads in the north west and south east, said restrictions may be needed on the Skye Bridge, Kessock Bridge, Dornoch Bridge, Cromarty Bridge and the Forth Road Bridge.
The Queensferry Crossing will also be monitored for ice.
Ian Stewart, from Bear Scotland, said: “We are fully prepped and are closely monitoring conditions and will act quickly when required.
“Drivers of high-sided and wind-susceptible vehicles such as caravans and trailers should take particular care and check for restrictions.”