A number of schools are closed across north west on Tuesday.
SDLP assembly member for Foyle Mark H Durkan described conditions on the roads as “shambolic”.
However, the Department for Infrastructure said it salted its entire scheduled network overnight “with 7,000km directly benefiting”.
Temperatures plummeted overnight, with a Met Office yellow warning for snow and ice in place now until midday on Wednesday.
The organisation expects snow showers through Tuesday afternoon, continuing overnight and into Wednesday morning.
It has warned of several centimetres of snow at some low level areas with between 5-10cm over some higher areas.
In the Republic, warnings for snow and ice have also been issued across counties Donegal, Leitrim, and Sligo.
The Department for Infrastructure has been criticised for not being prepared despite the weather warning, with some saying not enough was done to keep salt boxes filled with grit.
Emergency services dealt with several road crashes in Derry on Monday night, including one on Creggan Road after a car reportedly collided with a gas box.
A number of primary schools in the city, including Long Tower, St Patrick’s Pennyburn and St Brigid’s Carnhill, are closed.
Translink bus services have also been affected by snow, with delays and disruption expected throughout the day.
Derry City and Strabane District Council also warned residents of possible disruption to a number of services, including bin collection.
It advised people to leave their bin out as normal and that those not emptied today will be emptied as conditions improve later this week.
All council cemeteries are also closed to the public on Tuesday except to facilitate burials.
Recycling centres and parks will be opened “when it is safe to do so”, the council added.
Speaking to BBC Radio Foyle, Mr Durkan said his office was inundated with calls for assistance and that the Department for Infrastructure (DfI) had “come up short”.
“It’s awful that schools are having to close because of the state of the roads around the district, it’s shambolic to be frank.
“There was chaos around the city last night, we were inundated with calls, photos and video footage of collisions.
“We do our best to relay these requests to DfI. In some instances I was able to assist personally on different streets with salt, but the bigger picture is that DfI have come up short here.”
Roads Service engineer Peter McParland defended the response to the conditions, saying staff had been working in salting shifts over the past 24 hours and that there were “no major incidents to report”.“All gritters have made it safely back to the depots and currently all main roads are open and passable with care, but I would stress that we can’t guarantee roads will be free of ice even after they’ve been salted,” he said.
Mr McParland added that rural roads remain “challenging”.
“The department salts around 7,000km of road – that equates to about 25% of the entire road network, but it carries 80% of the traffic.”
He said he was satisfied that everything was done that could have been done by his department.
“The gritters were out from 15:00 yesterday, in the north west they went out again after 20:00 after the snow showers and again at 02:00 this morning. There’s plenty of salt on the road, but salt needs traffic to activate it, so I expect that the roads will clear.”
The department said 5,500 salt bins and 58,000 grit piles were available for use by the public on a self-help basis.
It added that despite its best efforts it could not guarantee ice-free roads even after salting. It urged road-users to be mindful of the changing conditions and take care while travelling.
“The best advice is in the Highway Code, take extra care even if roads have been salted, be prepared for road conditions changing over short distances and take care when overtaking gritters,” its statement read.
Paddy Canning, a safety officer with Derry City Football Club, said it took almost two hours to travel from Dungiven to Derry on Monday night.
“It took me an hour and ten minutes just to travel probably a kilometre from the new temporary road,” he told BBC Radio Foyle.
Mr Canning said he did not see any snow ploughs or gritters along the way, but commended local residents who “came out with shovels and sand” to try to clear a sliproad and warn drivers about the conditions.
“The only thing that helped was local residents from Claudy had come up and were directing traffic.
“When you came off the Foreglen Road there was no way of stopping, the only way of stopping was the bridge, the overpass, there was no snow under it, so people were sliding down the hill until they hit that spot, then turned to get on to the bypass which was treacherous.
“There were quite a number of cars sliding into each other.”
Mr Canning criticised delays on the construction of A6, saying the road was not safe.
The 15-mile stretch is part of the A6 upgrade linking Derry and Belfast. DfI said key aspects of the project have yet to be completed.
“It’s laughable and wouldn’t be allowed to happen anywhere else. I have worked on the other side of the Glenshane for 20 years and it was a horrendous journey.
“The Roads Service have a duty of care to us all. Maybe I should have left work early but people have jobs to do and they expect their roads to be safe.
“It’s just total neglect.”
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