Low temperature service is a design case, no different than a steam-out or other hot operation. It can occur because of low ambient, autorefrigeration or other conditions- but the mere presence of low ambient is insufficient reason to specify low temperature carbon steel. There must be a design case, i.e. a pressure coincident with the low temperature, for it to be considered in the design of the vessel.
Will the vessel be operated under pressure at -40 C? If yes, then it needs to be designed with materials which meet the temperature requirements of the design code. Example: a propane bullet installed in a cold ambient environment.
Will the vessel be lifted at -40 C? If so, you're going to need to ensure that the lifting lugs aren't subject to brittle failure during the lift.
People often get confused when the ambient temperature may fall as low as -40 C, but any practical pressurized service conditions must be above that. The mere fact that a vessel will be put in an environment at low ambient conditions does not mean it needs to be designed for those conditions. As an exmaple, any vessel containing water is going to be heat traced and insulated, and if it is going to be taken out of service and allowed to cool to ambient temperature, it will be depressurized long before it gets down to anything near -40 C.
Structural steel is another matter entirely. I'm not a structural engineer, but I am unaware of a situation where a static structure (i.e. not a piece of lifting equipment or the like) is specified with low temperature carbon steel. To my understanding, what is usually done is heavier sections of ordinary carbon steels are used and more attention is given to points likely to crack during cold operation.