"Can Santa come leave a present under your they in Sims2? And what day is it,Christmas in the game?"

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http://compsimgames.about.com/od/thesims2strategyhelp/ss/santa_sims2.htm
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In order to get Santa to come for Christmas and leave a present, you will need to have "The Sims 2 Holiday Edition" or "The Sims 2 Holiday Party Pack" installed.

You will need to buy your Sims a Christmas Tree for Santa to arrive. The tree doesn't need to be placed anywhere special, just needs to be on the lot.

A Sim will need to bake Santa's Cookies sometime in the evening. Making the cookies in the evening, will cut down on the time you have to make sure the Sims don't eat all of them. Santa needs a cookie! Santa's Cookies can be found under the Serve Desserts menu on the fridge. A Sim needs to have one cooking skill and own stove with an oven. They can't bake cookies on the stove top.

Traditionally, everyone needs to be in bed for Santa to arrive and leave presents. I make my Sims get some sleep too. I send them to bed at 9, so they won't see Santa. Sims do not need to asleep for Santa to come.

Santa Clause will arrive at 10 PM and leave a present for the family. He will then eat a cookie, spend a few hours doing many belly laughs, and use the bathroom a few times. Sims will get a queue an action to see Santa. If you let the Sims see Santa, they will act surprised and then cheer.