It also warned of icy patches on some untreated roads and pavements, a risk of lightning strikes and possible brief power outages.
The warning - which covers most of Lancashire except Blackpool - will be in place from 8pm today (Thursday, January 6) until midday on Friday (January 7).
A spokesman for the Met Office said: "Frequent wintry showers arriving from the west during Thursday evening and overnight are likely to lead to a fresh covering of snow for areas above 200m (mainly around 2-5cm, possibly as much as 10cm over highest ground where showers are most frequent).
"Falling snow below this level may cause some temporary slushy accumulations which then may freeze and cause dangerous, icy patches where skies remain clear for long enough.
"Winds will be gusty around heavier showers and there is also a risk of lightning strikes from isolated thunderstorms in some coastal districts."
Here's what the Met Office said to expect:
- Travel delays on roads with a small chance of some stranded vehicles and passengers, along with delayed or cancelled rail and air travel
- There is a small chance that power cuts will occur and other services, such as mobile phone coverage, may be affected
- There is a slight chance that some rural communities could become cut off
- Probably icy patches on some untreated roads, pavements and cycle paths
The warning started at 10am today (Thursday, January 6) and will end at 4pm.
Forecasters predicted snow would fall for one to two hours, causing some travel disruption on higher routes.
"A band of rain will move eastwards across the UK during Thursday, with this likely to fall as snow for a time, particularly over hills," a spokesman for the Met Office added.
"Many places will see 1-2 hours of snow with a risk of temporary slushy accumulations above 100-150m with snow leading to difficult travel conditions.
"A longer period of snow is expected over higher ground with 2-5cm likely above 200-300m, and 10-15 cm above 400m.
"Over higher routes, strong winds will lead to drifting and temporary blizzard conditions."
What can we expect the weather to be like across the county over the next few days?
Today (January 6):
A cold start with sunny spells and the odd wintry flurry across Cumbria.
Strong winds, rain and hill snow will spread from the west late morning onwards.
This will clear eastwards late in the day followed by blustery wintry showers.
Maximum temperature 7C.
Tonight (January 6):
Further sleet and snow showers overnight accompanied by strong, gusty winds.
Snow may briefly fall even on low lying ground in heavier showers, with a risk of ice by morning.
Minimum temperature -1C.
Friday (January 7):
Sunny spells and wintry showers, some of which will be heavy and with a risk of hail and thunder.
Brisk winds will make it feel particularly cold.
Maximum temperature 5C.
Outlook for Saturday to Monday (January 8-10):
Windy and milder Saturday with periods of rain, clearing to showers later.
Becoming dry and bright on Sunday, but more rain arriving overnight.
Cloudy and mild Monday with patchy rain.
For unlimited access to our unrivalled local reporting, you can take out a subscription HERE and help support the work of our dedicated team of reporters.