1988 Bronco II computer codes

Yes, when engine coolant temp is under about 140degF computer runs Open Loop
But only O2 sensors are not used, O2 sensors need to be at or above 600degF to read oxygen levels correctly, which is why O2s are also heated, to get them up to temp ASAP

Computer runs factory air:fuel mix based on engine load(MAP sensor) and throttle position(TPS), in Open Loop
It also has an "offset" for Open Loop based on Closed Loop operation for the last 100 or so cycles, in newer computers it is Long Term Fuel Trim, so if fuel pressure is lower and there are a few small vacuum leaks this will "offset" the factory table mixes so engine runs the same, when brand new or 25 years old, in theory

If you haven't already I would replace ECT sensor
ECT(engine coolant temp) sensor is only used by the computer
Dash board gauge uses a SENDER, 1 wire

If ECT sensor is telling computer coolant is -20degF at cold start, and actual temp is 50degF, then engine won't run well until ECT reports correct temp.

ECT sensor tells computer what Cold Idle RPM to set and what Richer fuel mix to use, all cold engines need to be "Choked", run a richer mix and higher idle, fuel injection doesn't have Jets so can't use a Choke plate, so computer has to emulate "Choke"
And how much Choke to use is based on engine/coolant temp, same as it was on a carb

If you have replaced ECT then check voltages on its two wires
Use a sewing needle/pin to pierce one wire at a time
Key on
One wire will have 5volts, that the Reference voltage from the computer
Other wire will have Temp Voltage, called Return voltage
Look here: http://www.explorerforum.com/photopost/data/503/41928895.gif
50degF = 3.5v
140degF = 1.3v

Voltage will go down as coolant warms up
So check it cold then run engine for 2 or 3 minutes and shut it off then check it again
Then at full warm up check it

If you can check it cold with engine running, be careful, then you may see Return voltage jumping around, computer will react instantly to that so would account for wandering idle and Rich mix when cold
Could be 5v wire is shorting to Return wire, causing high and low voltage on return wire

I have an update. I checked the connector from the O2 sensor to the engine harness. I found one of the pins got pushed back in to the socket on the new O2 sensor connector. ( I think it was the heater pin ). I pulled the pin back out and plugged the connector back in and out a few times and now it is OK. I ran the engine and did not have any rich events, and the engine idled down quicker. I ran it for about 30 minutes and the CEL came back on. I scanned it and it still had the code 41. The next day I checked all of the vacuum line connections and found 2 that were kinda loose. One was the MAP sensor to the intake, the worse of the two was the FPR valve. The FPR was the only vacuum hose on the engine that is an original as it is an S shaped preformed factory line. I replaced it with new hose. I cleared the code 41 with the scanner. I have ran the engine for 3 separate times, 30 minutes each time and have not had the CEL come on. I am going to do the KOER scan next and see how that goes. I appreciate all of the excellent advice, and will update as I have new info.

Here is an update. I was still getting the code 41 HEGO not switching. I checked all of the O2 sensor wiring back to the computer. All of that checked out OK. The O2 sensor is new so I kind of ruled it out. I ran out of other things to check so I replaced the new O2 sensor with a new Bosch OEM O2 sensor. I have driven with the new O2 sensor for about a week and I have no symptoms of running rich and or surging when driving. Apparently the O2 sensor does have an effect on the engine in open loop or I should not have a difference with cold start symptoms. I also have not had the CEL come on. The only start up issue I still have is a little searching on cold start ( 15 seconds ) before the engine goes to fast idle, after that the engine runs fantastic.