Of all the weather elements, temperature seems to be the most important to players. While hot weather is preferable, the sand can get cold when the temperature drops.
While it can affect a player's handsets, rain will not stop players from competing. Rain mixed with hail, lightening, threat of tornadoes are examples of when a tournament can be delayed or cancelled.
Play will go on as long as it safe for the participants. Tournament directors make the decision on if play is delayed or a tournament is cancelled.
Unless the wind is associated with severe weather (tornadoes, lightening), then the game will go on.