I found that those three are all frequently used as I've searched each of them in NYT site. I wonder what's the difference among them in usage.
The examples are as below.
Cold spell:
Although this cold spell would not have been unusual before global warming, it is now a relatively rare event in any one region.
That first cold spell of the season always feels especially harsh.
How do you feel about the frigid cold spell gripping North America?
Cold snap:
With climate change warming the Arctic air, researchers say, cold snaps are getting warmer. The recent spell of cold was an outlier.
While temperatures across the country on Monday will remain below zero, the cold snap will start to break during the day Tuesday.
Slippery conditions as cold snap ends in most of Finland
Cold wave
The severest cold wave of this Winter is being experienced.
More than 270 people have died from a month-old cold wave in northern India
This warmth came despite a significant January cold wave in the eastern United States that brought copious snowfall to several regions.