So if you tell your kid "you'll get a cold" they get a cold? :)
I know you are discussing children, but this applies to adults too. I've heard so many times that its a myth, I've heard so many times that it isnt. I don't know what to believe, but all my colds/flus/variation of the two, without exception have followed freezing my ass off somehow, or i should say my throat.
I sometimes get a sore throat in the morning if it was too cold in the room where i sleep.
It is obviously a combination of both, yes it is viruses/bacteria, but the cold clearly does something bad to the immune system. Even in the US, look at the cold/flu "seasons". They come in each region, approximately when it suddenly gets cold every year.
As far as cold drinks, i think it is much harder to say. You are reducing blood flow (white blood cells = the immune system) to the mucous membranes, but is such a short time significant? Again, the answer would have to be a mix of lots of other factors.. No one will ever be convinced of anything 
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"Я это понимаю на рациональном уровне, но не могу принять на эмоциональном" --Бизнесмен Борис Березовский