If we look at the warning and analyse it closely, you get the sense that actually, the Met-office may well be concerned that snow could cause disruption to low levels too. The first wording they use is "Not currently expected to be disruptive at low level areas in most places".. this suggests actually yes there is a risk of heavy significant snow even down to low levels but it's too early to say, as it may change.. if they issue an amber warning, they may also alter the yellow warning for low areas, or perhaps, even include some low lying areas in the amber warning as they say "in some places" too, perhaps meaning..some low levels areas could see significant snow.. though at this current time, it is not expected.
The warning also says that lying snow could occur almost anywhere even at low levels, though here, amounts will be fairly small at 1-2cm. They also say it could be localised - which ties in well with the previous statement.
However they do say that the snowline will retreat during the day, as it will get milder - and places like Mid-Wales and West Midlands have been removed off the warning, so it is going to be further north than expected.