Most tires, even LTS do not say maximum cold inflation. They say maximum load XXXX number of pounds at maximum pressure that is printed on the sidewall . Some may add cold for uniformity.Step into the world of LT's. It is common to see MAX COLD which is not MAX.
Even Turf & lawn mower tires have a maximum inflation credit on the sidewall. The first post was that there was no maximum pressure printed on the sidewall. I can't recall ever seeing a tire even on a two-wheel dolly but didn't have maximum inflation printed on the sidewalk.
No tire should ever be inflated past the maximum pressure stated on the sidewall.
It is irrelevant if you're going to haul a heavy load or not. If your load is over the maximum load rated on the sidewall of the tire at the maximum pressure then you need a heavier Rated Tire.
For uniformity we always check tire pressures when cold. This is not to say that a tire inflated to 80 lb cold will not be a few pounds over when it has been driving on the road for several miles.
But you never put 82 or 85 lb in that same Tire when it's cold because you're going to haul more weight. That is not appropriate.