heavy, thick
fine, light
The plants were covered in fine snow.

deep
wet
compacted, crisp, frozen, hard, icy, packed
The crisp snow crunched as we walked through it.
The frozen snow was treacherous to walk on.

powder, powdery, slushy, soft
drifting, driving, falling, swirling
They struggled on through the driving snow.

melted, melting
fresh, freshly fallen, new, newly fallen
first
the first snow of winter

spring, winter
artificial, fake
They had to use artificial snow at the Winter Olympics.

dirty

flake
fall (esp. BrE), flurry
patch
dusting
There was a light dusting of snow on the ground.

blanket, carpet, layer
pile
There were great big piles of snow on the road outside.

foot, inch
The porch is currently covered in three feet of snow.
Three inches of snow had fallen.

handful
He grabbed a handful of snow and threw it at Kate.

be covered in
The car was completely covered in snow.

blow (AmE), clear (esp. BrE), plough/plow (esp. AmE), shovel (esp. AmE), sweep
She cleared the snow from the path.

melt
The sun came out and melted all the snow.

expect
We're expecting snow over the next few days.

get, have
Southern Europe rarely gets snow.

struggle through, trudge through, walk through
I trudged through the snow and ice to the edge of town.

cover sth, lie, pile, pile up, settle
Snow covered everything from horizon to horizon.
Snow had piled up against the walls of the house.
It was too warm for the snow to settle.

come down, drift, drive, fall, swirl
The heaviest snow is coming down in Maine.

melt, thaw

flurry, shower, storm (usually snowstorm)
conditions
The snow conditions were excellent.

fall (usually snowfall)
a heavy snowfall
a light snowfall
an area of low snowfall

cover
The glacier provides skiers with year-round snow cover.

line (usually snowline)
animals that live above the snowline

bank, drift (usually snowdrift)
He got his car stuck in a snowdrift.

field (usually snowfield)
slide (usually snowslide) (avalanche in BrE)
day (AmE)
Growing up in New York, I had my share of snow days.

blower (usually snowblower), plough/plow (usually snowplough/snowplow), shovel
cannon (BrE), gun
blindness
chains, tyre/tire
shoe (usually snowshoe)
globe
She bought a plastic snow globe with the Eiffel Tower inside.

across the snow
We walked across the snow to the road.

in snow, into snow
The children are playing in the snow.

through snow
We struggled through the deep snow back to the chalet.

under snow
The steps were buried under the snow.

hard, heavily
It had been snowing heavily all night.

lightly
outside
It looked to be snowing outside.

overnight
We woke up to find that it had snowed overnight.

begin to, start to

start snowing, stop snowing
It started snowing just as we were setting out.