If the game hasn't started yet, the home team manager has the authority to allow the game to play or not. I'm sure they do a weather check to find out what the conditions are before making such a call.
If the game has already started, it's the umpire's call. Again, they check to find out what the conditions are.
There is no set time as to how soon you will find out if a game is postponed. It all depends on the weather conditions and the call by the manager or umpire.
Tossed and checked for flaws
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