Grace212 ~ the GFS has had several runs where it shows something snowy around that date but it's way into the future to say for definite. The metoffice outlook mentions snow in the north/cold spells countrywide but isn't really committing to anything more. They think any possible snow/proper cold could be later/the last week of this month...
UK Outlook for Thursday 10 Jan 2019 to Saturday 19 Jan 2019:
Most areas will be dry on Thursday with some sunshine after an early frost. However, the far southeast will have rain showers and some rain will affect the northwest. On Friday cloud will extend to most parts from the northwest, accompanied by a rise in temperature. However, it will remain mostly dry, perhaps with heavier rain reaching the northwest later, where winds may also strengthen. Over the weekend and into the following week, the weather is set to become generally more changeable, with gales at times and bands of rain crossing from the west. Some snow is expected in the north, especially in brighter, showery, colder interludes between weather systems. The south and southeast can expect the best of any drier and brighter periods. Meanwhile, some frost is still likely.
UK Outlook for Sunday 20 Jan 2019 to Sunday 3 Feb 2019:
The period may start with predominantly wet and windy weather, and a chance of heavy rain and gales at times, especially in the north. Hill snow is also possible, as well as snow to lower levels at times in the north. In the south though, there could be some drier and brighter periods too. Temperatures will vary between mild and rather cold at times, with overnight frosts during settled spells. However, as the period progresses there is an increased likelihood of a change to much colder weather becoming established generally, bringing an enhanced risk of frost, fog and snow. These notably colder conditions are by no means certain though, and in any case, some milder, wet and windy interludes are still possible.