Disruption is expected until Saturday and National Rail has advised travellers to check before they travel.
On the roads, the storm also hit rail replacement services, and roadside assistance companies reported a busy day with a high number of callouts on Friday.
The cold weather alert is in place from 8am on Monday November 17 until 8am on Friday November 21 and covers the East Midlands, West Midlands, North East, North West and Yorkshire and The Humber.
Met Office meteorologist Honor Criswick said: “Overnight (on) Saturday and throughout the course of Sunday, we will start to see winds changing to be a bit more northerly, introducing a lot of Arctic air.
“Clouds will clear throughout the course of the day so it will allow for some sunshine, but with it, it’s going to be turning much colder.
“I think people are really going to notice a chill into Sunday and feeling cold in many areas.
“Things are starting to turn less stormy, a bit brighter, but it’s going to be feeling a lot colder and, as we head into next week, we’ll see a continuation of that.”
