We were told by our concrete contractor the weather is getting cold and he will have to charge more for his work in cold weather, is this true?
I suspect he is correct, if you have a contract for a lump sum he cannot charge you more, but if the contract has a provision for cold weather concreting, he may be able to charge you more money. Cold weather is defined in American Concrete Institute 306. Here is some "man in the street" language, it says "a period of time when for more than 72 hours straight, the average daily air temperature is less than 40 deg. F."
Concrete needs to be protected from freezing and should be kept above the 40 deg. F temperature during the critical curing period. I imagine your contractor is thinking about the extra expense of ordering concrete mixed with hot water and once the concrete is in place, protecting it with blankets to prevent freezing. This will be an extra expense, who pays it? I do not know.