The warning comes as two drivers were stopped for driving at around 100mph on the M8 last night during what police described as extremely poor conditions.
Meanwhile, flood alerts have been issued for coastal areas still recovering from severe weekend storms. Heavy rain and strong winds are also expected to hit central Scotland over the next two days.
The Met Office has amber "be prepared" weather warnings in place for central Scotland while yellow "be aware" warnings cover much of the rest of the country. Snow could fall in the highest areas, forecasters added.
Strathclyde Police issued a warning to drivers today about the dangers of speeding during adverse weather.
The force said officers stopped two drivers on the westbound M8 between junctions 13 and 16. The men were said to be driving at speeds of 98mph and more than 100mph in a 50mph zone.
Superintendent Jim Baird said: "If you drive in excess of the speed limit you risk not just your life, but other road users' lives also. To do so in such poor weather and road conditions is just plain dangerous and is unacceptable."
He added: "Those conditions last night were extremely poor, in terms of visibility and the probability of, unexpectedly, encountering surface water.
"If you drive dangerously, you are likely to be caught. Please respect the speed limits, the road conditions and drive safely so that you, your passengers and other road users are not put in danger because of your driving."
Tayside Police said rain had been falling across the region today, with a build-up of surface water on roads across Angus, Dundee and Perth and Kinross.
Officers warned of a potential risk of river flooding, with the overall conditions expected to result in large waves - potentially up to five metres along the coast line.
Council workers in the area have been checking gullies, ditches and drains as well as distributing flood warning signs and sandbags.
Gale-force winds and high tides forced the evacuation of dozens of people from their homes and caused millions of pounds worth of damage in the east of the country on Saturday and Sunday.
Ports and flood defences were damaged in Aberdeenshire and Berwick in what environment minister Paul Wheelhouse described as a "perfect storm" of low pressure, high tides and gales.
The Scottish Environment Protection Agency (Sepa) is now warning of potential flooding throughout today and tomorrow.
Sepa hydrology manager Vincent Fitzsimons said: "There is a coastal flood risk for the latter part of Thursday and throughout Friday for the north and east coastlines.
"Areas affected last weekend could again be affected and waves of around five metres are possible throughout these areas, with potential for larger waves from Stonehaven northwards to Orkney.
"Elsewhere, heavy persistent rain and gale force south-easterly winds could affect the Southern Uplands and areas around the central belt such as Stirlingshire, Tayside and Angus."
During the storm on Friday, a crewman aboard North Sea stand-by vessel the Vos Sailor died after the boat suffered serious damage, and 11 others had to be winched to safety.
About 60 people were evacuated from properties in Stonehaven and Peterhead and harbour walls and some commercial properties were badly damaged along the east coast.
Aberdeenshire Council is urging people to avoid harbour areas over the next couple of days if possible.
Mr Wheelhouse said the Scottish Government's resilience team is closely monitoring developments to deliver a co-ordinated response.