John Swinney’s comments come after he chaired a Scottish Government Resilience meeting around the storm impact on Thursday night.
The Met Office issued a yellow warning for snow covering much of mainland Scotland. This came into force at 3am today and is due to lift on Friday at 6pm.
Travel is likely to be affected, and the forecaster has warned that vehicles and passengers could be stranded on the road due to heavy snow. They also anticipate delayed or cancelled rail and air travel.
Speaking to BBC’s Good Morning Scotland, Mr Swinney said: “There’s obviously challenging conditions because of very heavy snowfall overnight.
"It was forecast and the trunk road operating companies and our partners in local authorities have been undertaking extensive gritting operations over the course of the night to try to make sure that the travel this morning was able to be sustainable on the road.
“There’s obviously a few problems in different parts of the country but there are gritters getting to these issues very quickly and trying to resolve them but undoubtedly the advice that was issued last night about ensuring that people check the conditions before they travel is advice that should be followed today in all circumstances given the volume of snow that is currently falling.”
Asked if the measures taken across networks are proportionate, Mr Swinney said: “We have an immensely more sophisticated amount of information that’s readily available to every member of the public.
“What we’ve got to be careful about is making sure that the warnings are proportionate to the conditions that are faced.
“An amber warning, for example, required ScotRail to cancel all services the other day and when you looked at the damage that was done on the network that looked to me to be a proportionate decision that ScotRail took as I wouldn’t want a train hit by debris that was lying around.”
Mr Swinney said extensive preparations are currently being put in place and resources are available if there are any welfare situations.
The deputy First Minister confirmed the storm has followed the path the Scottish Government modellers predicted in causing destruction.
He said: “The snow has swept through the country and there will be heavy snow for most of the day.
“In relation to the preparations, obviously the trunk road operating companies were all activated and they had their plans in place last night.
“The power companies likewise are ready for the impact of the other part of the forecast which was about strong winds in case there is any damage to power supplies.”
Mr Swinney said a “particularly localised worry” is in the South of Scotland where there is a prediction of coastal flooding in the south west in Dumfries and Galloway area because of the strength of the wind within the Irish sea and area in the Solway Firth.
“There is obviously a need to be very careful in coastal situations down in the south-west.” said the deputy First Minister.