Motorists have been facing disruption on many routes as extreme weather hit large parts of the country, while those on the M80 have been at a standstill for a number of hours.
People had been told to avoid travelling after the warnings for heavy snow and ice were issued - including the highest level red alert in central parts of Scotland
Speaking to Reporting Scotland, Mr Yousaf said: “Some employers have been extremely flexible, but clearly some haven’t.
“There will be some conversations I’ll be having after this weather event because I have seen HGVs that are carrying home furniture, stationery and piping.
“Now, I’m not convinced that that is all necessary and many of the incidents we’ve seen have involved a loss of traction from HGVs.”
The Met Office warnings cover most of the country including central Scotland, Tayside and Fife, south west Scotland, the Lothians and Borders and Strathclyde areas.
Betterthanzero said it had been “inundated” with messages from people working in the hospitality sector saying they were being “forced” to travel to work.
The Scottish trade union group claimed employees could use legislation as a basis for refusing to make the journey, over safety fears.
Extreme conditions are expected in red alert areas between 3pm on Wednesday and 10am on Thursday, while an amber warning for snow is in place across central, eastern and northern parts of the country until 6pm on Thursday.
A further meeting of the Scottish Government’s Resilience Room has been held, chaired by the Deputy First Minister and attended by Mr Yousaf, to prepare for the forecast.
Disruption has seen NHS Greater Glasgow and Clyde announce all non-essential operations and outpatient appointments for Thursday would be rearranged.
First Glasgow halted its bus services at 3pm due to the snow, while Stagecoach called off its operations in Fife for the remainder of Wednesday.
It is the first red alert for snow in Scotland since a new warning system came into place in 2011.
The definition of a red warning is “you should take action now to keep yourself and others safe from the impact of the weather” and it cautions that widespread damage, disruption and risk to life is likely.
The warnings come as hundreds of schools across Scotland were closed and there was severe disruption on the road and rail network as a result of heavy snow in large parts of Scotland on Wednesday.
A number of councils have already announced that their schools will be closed on Thursday.
In addition to schools, some universities and nurseries have also been forced to close.
Virgin Trains said services between Scotland and England have been cancelled for Wednesday and Thursday.
ScotRail halted operations in the red warning area between 6pm on Wednesday and late Thursday morning.
The weather also affected flights across Scotland’s major airports, with Glasgow Airport suspending all operations until later on Thursday.
British Red Cross emergency response volunteers in Glasgow were supplying bedding for up to 100 people in case they were stranded overnight.
The SPFL announced that Wednesday night’s games in the Ladbrokes Premiership - Celtic v Dundee, Hibernian v Hamilton Academical, Motherwell v Aberdeen - have been postponed.
Of the red warning, the Met Office stated: “Roads will become blocked by deep snow, with many stranded vehicles and passengers.
“Long delays and cancellations on bus, rail and air travel are expected. Some communities could become cut off for several days. “
Forecasters warned that lying snow could reach 20-30cm and possibly 40cm in a few places by mid morning on Thursday.
This is the first red alert for snow in Scotland under the new warning system. There have been red warnings for wind and rain north of the border before, the Met Office confirmed.