Here's a quick look at the situation, from the 12z actuals and predictions.
First off, the wider european plot:
The low pressure is positioned in Sweden with a central pressure of 981 hPa. The warm and cold fronts can clearly be seen by the kinks in the isobars.
Here is the corresponding satellite image:
You can clearly see the differing air masses there, well specifically you are seeing the height of the cloud tops - the IR image shows the temperature of the water vapour.
If we take the satellite with precipitation overlaid:
I would draw on the fronts roughly like this:
Now. if we zoom in on the UK surface analysis, we can see the temperature drops behind the cold front. Widely 5-7c before the front and 2-4c immediately behind with that dropping down to 0-1c by the Borders and widely below 0c in Scotland as the cold air digs in.
Lastly, we can compare the actual results with predictions from the GFS and the NAE. Here is the GFS prediction:
Here is the NAE prediction:
Comparing these they seem pretty close. The GFS, because of its resolution looks like more of a broad-brush of where the precipitation will be - not bad. The NAE also looks a bit broad and has slightly underestimated the speed of the front and overestimated the precipitation but otherwise not bad all round. One last image - the UKMO surface pressure chart for 12z, which looks pretty close to me (as you'd expect at this range):
What will be interesting to see later on is how much back edge snow (if any) there is towards the South and whether the front largely fizzles out - it doesn't look particularly vigorous to me (yet).