There is a lot of snow outside. Hence, children should not go outside. There is a lot of rain outside. The children, therefore, should not go outside. There is a wind outside. Thus, children should not go outside. There is a chilly weather outside. That is why, the children should not go outside. I think comma is unnecessary in all the sentences here that have the second sentence as a single continuous unit. Only the second sentence has a break due to the use of 'therefore', making the use of comma warranted. Also, Instead of Hence and Thus, you would be better off when using therefore. Hence and thus are by common usage interchangeable, however according to the rules of grammar they are different. Hence should indicate future use - such as "Hence we will proceed as described." Thus should indicate the past in its usage, or to indicate a conclusion, such as, "The British and American troops fought to a standstill, thus no winner was declared." See this link for more information: http://painintheenglish.com/case/4452

For me only the example with 'therefore' is correct. I would not use commas with any of the others. In the basic sentence "The children should not go outside 'therefore' is inserted as a little extra, and should be surrounded by commas to mark it off as such. The same is true of 'however'. In the last example the part after 'why' is an indirect question. "Why should the children not go outside?" is a direct (original speech quoted) question. "I do not know why the children should not go outside" contains an indirect question (original question is used as part of the statement, and 'why the children should not go outside ' is one unit). The same system is good for all other question words, not just 'why'. E.g. no commas in any of these - I would like to know WHERE she went. Do you know HOW MUCH they paid for it? He did not tell us WHEN he would be back. They are trying to find out WHO did it. Personally I would avoid "thus" like the plague. A bit olde worlde. :D