A band of heavy rain and hill snow will increasingly turn to snow at lower levels as it moves east through Tuesday morning and early afternoon.
Some roads and railways are likely to be affected by snow with longer journey times by road, bus and train services.
Some flooding on roads is also possible.
A Met Office spokesman said: “A band of heavy rain will spread eastwards during Tuesday morning and early afternoon, quickly turning to snow on high level routes above 200 metres and to lower levels for a time before it clears.
Accumulations of 5-10cm of snow are likely above 300 metres, much of this falling in a short period.
“15 cm may accumulate on the highest routes above 400 metres.
“At lower levels, amounts will be much more variable with a few cm possible in some places while others will just see sleet and rain.”