drizzle (n) / drizzly (adj) - моросящий дождь
very soft, light rain, which usually continues for a long time

pouring (adj) - ливень
raining very heavily

sleet (n) - дождь со снегом
freezing rain; a mixture of rain and snow together

It's chucking it down! - Льет как из ведра!

It's raining really heavily  

Nice weather for ducks! - Хорошая погодка для уток:)
It's raining very heavily

boiling (adj) - очень жаркий
very hot

sweltering (adj) - очень жаркий
very hot

scorching (adj) / a scorcher (n) - знойный
extremely hot

a heatwave (n) - жара
a period of extremely hot and dry weather that lasts for several days or even weeks

chilly (adj) - прохладно
quite cold

freezing (adj) - очень холодно
very cold

frost (n) / frosty (adj) - мороз/морозно
this is the name for the layer of ice crystals that forms on exposed objects when the weather's very cold. This often happens overnight, and when you wake up in the morning everything's white!

icicle (n) - сосулька
the kind-of pointed stick of ice which is formed by the freezing of dripping water.

breeze (n) / breezy (adj) - бриз, легкий ветерок
a light wind, and is often quite refreshing when the weather is hot

blowy (adj) - ветрено
quite windy

blustery (adj) - порывы ветра
wind blowing in short but strong and frequent bursts

high winds - сильный ветер
strong winds