It says old, not cold.

You're correct. I misread what he posted. I though he said "when engine is cold" but he said "when engine is old". I wish he'd say "worn" instead of "old" because it's the wear/condition/circumstances of the engine that matter, not the age.
Now that I've read that correctly, I'll answer what he was really asking. It doesn't matter how old the engine is. What matters is the condition/wear/circumstances of the engine. If the engine is leaking or burning oil, or having fuel dilution, that is when many say to increase the oil viscosity. Specifically to increase the 2nd # after the w by 1 grade.
For example: My car is older than my 2 neighbors' cars, but my car engine is in much better condition than their cars.
My car is in good condition (no oil leaking, no oil burning, no fuel dilution). So I continue using stock viscosity oil for it, which is 5w30.
One neighbor's 03 Honda CR-V 2.4L loses 5w20 oil
rapidly. I still haven't conclusively diagnosed it, but stuck rings and oil burning are likely causes. Diagnoses is ongoing. Along with a few other fixes, I will also change it's oil from 5w20 regular oil to 5w30 VRP for 4 OCI. Then change to Quaker State Ulimate Protection Full Syn (QSUPFS) 5w30 (which has
higher KV100 cSt op temp viscosity than other 5w30 full syn USA oils). Also, she drives exclusively city miles. So I will decrease OCI from ? to 3.5K miles, which will be about 2 years for her.
My other neighbor's 11 Hyundai Elantra 1.8L has been having a severe fuel dilution problem (watery thin, black, stinky used oil). She was using a 5K OCI and 5w20 regular oil. I will switch it to 5w30 VRP for 1 OCI. Then 5w30 QSUPFS after that. She drives exclusively city miles. So I'll decrease her OCI from 5K to 3.5K, which will be about 2 years for her.
I had a worn out push lawn mower than burned 30 grade oil like crazy (far worse than my neighbor's CR-V). So I changed the lawnmower oil to 40 grade. Then much less blue smoke and much less oil consumption. It worked well using 40 grade for many more years with no problems. The mower frame finally broke. So the engine outlasted the frame, but only because increasing oil grade from 30 to 40 gave the engine more years of good service life.