A cold morning slows the clock down, not just the crew
Concrete gains strength through a chemical reaction between cement and water, and that reaction runs slower in cold weather, the same way most chemistry does. A slab that would take on enough strength to resist frost in a normal set time can sit vulnerable far longer on a cold morning, and freshly placed concrete that freezes before it has gained enough strength can be damaged for good. An accelerator pushes that early strength gain to happen faster, closing the window where cold weather can do harm.
It does not change what the concrete ends up at once it is fully cured. What it changes is how fast it gets there, which on a cold pour is the part that actually matters. Timing has real consequences on a cold job. A footing that has not gained enough strength before an overnight freeze can suffer damage that shows up later, well after the crew has moved on, which is exactly what an accelerator is there to prevent.
Accelerators change the clock on a pumped load too
Set time additions are not just a curing question. Anything that speeds a load up also shortens how long that concrete can sit still in a hose before it turns into a problem, which is exactly the kind of detail that has to go on the order rather than get discovered at the hopper. If a job is being pumped and it needs an accelerator, both facts belong on the same ticket, since the plant and the crew are both working against the same clock.
What kind of accelerator goes in is the plant's call
There is more than one way to accelerate a mix, and which one fits a given job is a mix design decision made at the plant, not a preference to hand-pick off a glossary page. What matters on your end is saying the concrete needs to move faster in cold conditions when you book it, and letting the mix design people choose the right tool for that particular pour.