A Met Office weather warning for snow is in place between 3am and 6pm on Friday, while a wind warning encompasses the south-west Scottish borders, including most of Dumfries and Galloway.
Snow is forecast throughout the day for most of mainland Scotland south of Inverness and Fort William, and was disrupting travel on Friday morning.
The M8 was closed eastbound at junction five due to the heavy snow and Traffic Scotland tweeted that there were reports of vehicles getting stuck on the A68 near Soutra.
Bear Scotland North West Trunk Roads reported heavy snow across the north-west network, including the A83 Rest And Be Thankful, A82 Glencoe, A85 Glen Ogle, and A889 Catlodge.
In Aberdeenshire more than 30 schools were closed due to the forecast heavy snow while some schools were shut in Angus and Inverclyde.
Ferry passengers also faced disruption on Friday due to adverse weather.
Caledonian MacBrayne said that some services were liable to disruption or cancellation at short notice due to the conditions.
Storm Eunice follows strong winds from Storm Dudley that caused significant disruption to rail and ferry services, with trees blown on to train tracks and overhead power lines.
Scotland’s Deputy First Minister John Swinney said he chaired a meeting of the Scottish Government’s resilience team and that Storm Eunice “will bring risk of snow and strong winds across most of Scotland on Friday and danger of coastal flooding in south-west Scotland”.
He added: “Please follow all advice and only travel if safe to so do.”
With more than 20cm of snow predicted on higher ground and 5cm elsewhere, Scottish Mountain Rescue warned there was a risk of “dangerous conditions”, including the possibility of avalanches.
The organisation’s vice chairman Kev Mitchell said: “The weekend forecast is for very unsettled and, at times, dangerous conditions.
“With the arrival of Storm Eunice on Friday, hills will see high winds and the potential for snowfall to low levels meaning the avalanche forecast will be likely to worsen.
“Good decision-making is key in these situations and often the decision not to go, whilst correct, is the hardest one to make.”
Specialist mountain weather forecasts are predicting sustained periods of gales or hurricane-force winds on higher terrain for the next week, with snow, rain and hail expected most days.
Mountaineering Scotland’s safety adviser Ben Gibson said: “With such extreme weather being forecast it’s important to plan your journeys around conditions rather than just going for long-held ambitions.
“Check the specialist mountain forecasts and what the Scottish Avalanche Information Service says, and take an honest look at your fitness and skill levels – and those of the others in your party – and consider whether your planned route is really attainable or whether you should adapt it or make different plans altogether.”
Despite the snow forecast, ScotRail said it does not expect the same levels of disruption from Storm Eunice as from Storm Dudley but has pre-emptively announced some trains will not be running.
Glasgow and Edinburgh trains to Arbroath and Montrose to Aberdeen services will not run because sets of points on the line that allow trains to move tracks are not fitted with heaters, meaning they could freeze and get stuck.
David Simpson, operations director at ScotRail Alliance, told BBC Radio Scotland’s Good Morning Scotland programme just after 8am: “Services are running very well at present, we are running a full timetable on the vast majority of routes and it’s running well.”
Network Rail Scotland announced it has five locomotives fitted with snow ploughs to use as required. It is proactively spraying de-icer on key junctions and extra staff will be deployed to deal with any problems.
The Met Office yellow alert for Friday warns there is a chance of travel delays on roads, possibly with stranded vehicles and passengers, along with delayed or cancelled rail and air travel and a slight chance that some rural communities could be temporarily cut off.
Forecasters said there is a small chance of power cuts and that other services, such as mobile phone coverage, may be affected.