Transport delays, treacherous driving conditions and school closures will greet many people as they return to work and study after the Christmas break, with winter weather warnings in place across the UK.

Four amber warnings for heavy snow in northern Scotland are in place until Monday morning, while yellow snow and ice warnings cover all of Northern Ireland, Wales and much of England.

Forecasters said there could be 30cm of snow on high ground in Scotland overnight and people living in amber warning areas could expect travel disruption and the possibility of rural communities being cut off.

Schools on the Shetland Islands will be closed on Monday while schools in Aberdeen will not open until 11am.

Loganair cancelled its flights from Inverness and Aberdeen airports on Sunday and offered customers the opportunity to change their plans without charge.

Transport Scotland urged drivers to carefully plan their journeys, leave extra time if needed and “drive to the conditions”.

Police Scotland’s assistant chief constable Alan Waddell said: “The forecasted heavy snow showers and ice means driving conditions are likely to be hazardous in some areas. Our advice is to plan ahead and consider if your journey is really necessary during the weather warnings.”

The Scottish transport secretary, Fiona Hyslop, said: “We’ve already seen challenging conditions and freezing temperatures, with more snow and ice on the way for the same areas. Of course for many Monday marks a return to work from the festive break. If you have to travel then please ensure your vehicle is winter ready and have a winter kit in your car.”

She thanked the gritter drivers, chainsaw gangs, police and others who had been out in force over the weekend.

Matthew Lehnert, a Met Office chief meteorologist, said that elsewhere in the UK there would be snow showers, ice and frost but “milder air will make attempts to spread eastward” from Tuesday.

He added: “This will mean rain becomes more likely in the south, but there is also the possibility of more organised snow along the boundary of the mild and cold air masses. Strong winds could also be a feature later in the week.”

The UK Health Security Agency (UKHSA) has issued amber cold health alerts across England until Tuesday.

Agostinho Sousa, the head of extreme events and health protection at the agency, said it was vital to check in with family, friends and neighbours who were most vulnerable.

He said: “The forecast temperatures can have a serious impact on the health of some people, leading to increased risk of heart attacks, strokes and chest infections, particularly for individuals over the age of 65 and those with pre-existing health conditions.”