The GFS is struggling (along with other models) with this one!
The scenario for a risk of snow next Tuesday remains, but the GFS is now leaning towards the idea of it being in the form of wintry showers. Chart below shows the NW flow with a trough moving south.
It's making much less of the shallow low feature spinning up on the north side of the jet on Tuesday morning (see below for 00Z GFS), which is what it originally saw as the potential for a more significant separate low feature crossing southern England.
This shows how uncertain things are for next week at this stage.
Best to work on the cool ideas, with the possibility of some snow, mostly in the northern half of the UK.
We'll see how things progress!