More snow warnings have been issued for tomorrow, but forecasters said milder weather lay ahead with temperatures up to 12C by midweek.
The expected end of a week-long cold snap follows heavy snow across southern Scotland that prompted police to tell drivers to stay off the roads.
Long queues built up on major roads as commuters, urged to leave work early, slithered home.
Vehicles struggling in the conditions caused hold-ups, including on the M77 south of Glasgow. There was major disruption on the M74 in South Lanarkshire last night after a lorry crashed through the central reservation barrier.
North-bound traffic was able to pass the scene in lane one, while motorists heading in the opposite direction had to use the hard shoulder.
Stagecoach suspended its Kilmarnock-Stewarton service as the A735 was closed between Kilmaurs and Stewarton.
Many schools, councils and universities closed early.
ScotRail passengers were delayed more than an hour on the Glasgow-Oban/Mallaig line at Crianlarich.
Amber and yellow severe weather warnings were in force for much of Scotland until 10pm last night.
They were followed by a yellow warning for ice across the whole country, apart from the north east, from midnight to 10am today, with up to another 3cm of snow also forecast.
More snow is expected tomorrow, when another yellow warning will be in force from 6am to 6pm over most of inland Scotland south of the Highlands.
The Met Office said 1cm-3cm was expected over lower ground and 3cm-15cm at higher levels.
Its warning stated: “The snow is more likely to affect higher routes, with lower levels only affected more locally.
“In addition, rain may fall onto frozen surfaces for a time, following a very cold night. Some roads and railways are likely to be affected, with longer journey times by road, bus and train services.
“The snow is expected to become confined to north-east Scotland later in the day as it progressively turns to rain from the south-west.”
Grahame Madge said: “With further snow and freezing conditions anticipated during Sunday, many will be looking towards the south and west for the promise of a respite and a return to warmer temperatures for the next few days.
“A warm front approaching the UK will begin to have an influence on temperatures across Scotland, which by the middle of next week could be approaching double figures in some locations, with a high of possibly 11C or 12C.
“The outlook will remain changeable with frequent rain, but with brighter periods.”