You bring up a valid concern about what the minimum temp should be. From my research, optimum ATF temps are around 170 F. The FSM says normal operating temp is 158-176. Even before I installed my external trans cooler, I would see temps in the 130's cruising down the highway on a mild temp day. The temperature your trans runs at depends on a lot of factors, ambient temp, speed of travel (air flow through the radiator and/or trans cooler cooling fins, strain on the trans (climbing grades), input from driver (turning OD off).
What most experts agree on is HEAT is the big killer of auto transmissions. Yes, having it run too cold all the time could allow moisture to build up in the trans and maybe the internal parts aren't lubricated as optimally at lower temps, but overheating your trans and not renewing the fluid on a regular basis are the real killers.
In regards to running too cold, external trans cooler manufacturers don't recommend bypassing the stock cooler in the radiator, especially if you live in cold climates because you lose some of the fluid heat transfer that happens with the trans cooler bathed in the hot engine coolant.
My B&M 70264 trans cooler allows my trans to run around 20 degrees cooler which can make a pretty big difference when you're climbing grades or towing. Since you're in Chicago with cold winters, your concern is legitimate. The coolers like mine have a low-temperature bypass that's suppose to divert the thicker fluid straight through cooler and not allow the fluid into the cooling fin channels until it thins out as it heats up.