どんよりした空模様って英語でなんて言うの？

In order to describe a sky that is covered in clouds and may rain, you can say:
An overcast sky
Overcast means cloudy or covered over with clouds.
'The sky looks overcast today.'

You can also simply say:
It looks like a cloudy day.
The sky looks cloudy.

Another phrase is:
The weather looks gloomy
Gloomy means miserable, sad, downcast.
This word is often used in the UK to describe cloudy or rainy weather.

British people also say 'muggy'
This has a similar meaning to gloomy. It means miserable, murky, dark and gloomy.
We are having some muggy weather today.
The weather looks quite muggy today.

I hope that helps!

Cloudy sky - the sky is full of clouds
"The sky is very cloudy today. I hope it does not rain."
Dark sky - usually refers to a sky that is covered with dark rain clouds
"There is a dark sky outside. You should take an umbrella to work."
Ominous - giving the impression that something bad will happen; if the sky/clouds look ominous, that means that it looks as if it will rain or there will be a storm
"The sky is full of ominous clouds. I think it is not a good idea to go to the park today."

A 'threatening sky' would be one full of low, dark clouds and possibly reduced visibility.
'Ominous clouds' - These two words are often used together. 'Ominous' means giving the worrying impression that something bad is going to happen; threateningly inauspicious. 'There were ominous dark clouds gathering overhead'.
'A sky with pregnant clouds.' This is a phrase that would more likely be used in poetry or creative writing:
poet David Rubadiri Poet's

An Africa Thunderstorm - Poem by David Rubadiri

From the west
Clouds come hurrying with the wind
Turning sharply
Here and there
Like a plague of locusts
Whirling,
Tossing up things on its tail
Like a madman chasing nothing.

Pregnant clouds
Ride stately on its back,
Gathering to perch on hills
Like sinister dark wings;
The wind whistles by
And trees bend to let it pass.

Cloudy describes a sky with lots of clouds in it, you can also call such a sky as overcast. To say there is a 'chance' of rain is to say that it is likely that it will rain.

Examples
"The sky looks really grey and dull today."
or
"What a cloudy dull day. "
or
"It is a dull grey day. "

"a gray sky" is a phrase we can use to describe a cloudy sky that looks like it might rainy.