Trans fluid gets very thick at cold temperatures (it can be like Vaseline® at very cold temps). The individual passages in the cooler are much smaller than the cooler lines, so thick ("frozen") trans fluid may not flow through the cooler at all, when temps are very low.
The hot oil from the torque converter is fed directly to the cooler, so if this circuit is deadheaded (due to a plugged, i.e. "frozen" cooler), the converter can quickly overheat.
A Thermal Bypass Valve (TBV) will allow flow through the cooler line circuit (bypassing the cooler), so it allows the hot oil to reach the trans sump (rather than just toasting the converter). But with basically no oil cooler, the trans will still overheat eventually. So to minimize heat generation within the converter, we use the modified shift schedule, to avoid overheating the trans. The modified schedule locks the TCC as much as possible, but when unlocked (generating heat), it maintains a lower-than-normal gear, since T/C slip (and the amount of heat generated) will be significantly less in a lower gear.
So, the TBV gets the hot oil out of the converter. The modified shift schedule prevents this hot oil (which is dumped into the sump) from overheating the trans.
The trans oil cooler is an air-to-oil cooler (not a traditional "in tank" water-to-oil cooler), so it is continually exposed to cold (ambient) air, even when the engine is warmed up. Thus, having the engine warm is no guarantee that the cooler will be "unfrozen." That's why we base the modified shift schedule on the ambient temp, rather than the trans or engine temp.