The issue at low temperature is catastrophic failure of the vessel due to a pre-existing micro-crack growing at the speed of sound ( in the metal) due to complete lack of fracture toughness. The 2 fatal events that I know of are (a) a feedwater heater shell hydrotest in Dansville NY in the winter , shell failed and fell on a worker killing him and (b) the Florida steam drum failure circa 1970 when hdyrotested. Both events were winter hydrotests, and the testing company did not meet the ASME-required minimum hydro test temperature .
From the many failures ( and hundreds of worker deaths) of the North Sea oil platforms of the 1960's and 1970's it was found that every weld contains at least 2 pre-existing micro-cracks, from the initial weld arc and from breaking the final weld arc. The stress concentration factor at the edge of a crack is roughly 5, and during a hydrotest the average metal is close to yield stress. Insufficient fracture toughness combined with a crack edge stress on the order of 4-5 times yield stress is a formula for failure. In addition to that issue, is the separate issue that many welds are not stress relieved.
So the matter is not so much allowable stress as it is fracture mechanics.
"Whom the gods would destroy, they first make mad "