Today's GameTalk asks you about the weather (http://grogheads.com/?p=8091)
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I think it has a place in all levels of game. The biggest drawback I've seen in games is when the weather conditions simply slow everything down and make it that much harder to get into contact, without any real purpose to the scenario.
When you're playing a 4 hour minis game, having snow/mud conditions that reduce everything to half or a quarter movement can make it almost impossible to a get into the action. Spending 6-8 turns just trying to get into range of the enemy isn't much fun. Especially when it's a 10 turn scenario :P
As is the case with so many things in games, it's all in the implementation.
My personal favorite example of weather affecting gameplay on the tactical level is (no surprise) the Total War series. Unfortunately, I can't really think of a game I've played where weather mattered at the strategic/operational level, at least not done well.
Weather can have really important effects on battle.
http://esoterx.com/2015/06/29/its-raining-pseudohistory-marcus-aurelius-and-the-quadi/