The warning is in effect from Tuesday 15:00 to Wednesday 08:00. At low levels throughout the warning area, 5-10 cm will be more typical.
The Met Office said: "Snow showers are expected during Wednesday evening before a spell of more persistent and possibly heavy snow develops in places during Wednesday night".
"This is the problem with the storm naming system", he wrote.
Storm Fionn will bring 80mph gusts, as well as eight inches of snow throughout the North West and North East of England, as well as Scotland, where an amber weather warning is in place.
Heavy snow in Scotland, Northern Ireland and northern England has shut schools and left hundreds of drivers trapped on roads amid freezing temperatures as low as -4C.
Meanwhile, today will remain very cold throughout the afternoon with widespread wintry showers over higher ground, some heavy with a risk of thunder.
Snow in the Pennines.
It cautions that injuries and danger to life from flying debris are possible, along with some damage to buildings.
Forecasters from the Met Office have warned of large waves along the coast, with "beach material being thrown onto sea fronts, coastal roads, and properties". The strongest winds are expected to transfer eastwards across the warning area before clearing by late morning.
Met Eireann and the Met Office revealed their Winter Storm names for 2017-2018 in September.
The Windy Gap route in Mayo was closed off on Tuesday night due to the weather conditions, and some roads in Monaghan were impassable due to snowfall.
"A deepening area of low pressure is likely to sweep across the Atlantic to affect the United Kingdom on Wednesday night into Thursday", the Met Office said. You've got a storm to ride out.