Justsome,
Things will also freeze if you take a wet aeroplane into sub-zero conditions as I did.
The exposure to icing conditions was less than 5 minutes; I experienced not more than light airframe icing (may have been severe if I had stayed there). The frozen trim was not due to airframe icing but sub-zero air temperature otherwise it would have unfrozen at a similar rate to the rest of the ice on the aeroplane. Trim tabs are on the trailing edge of the surface. You're in a bad way if the ice has water frozen as far back as that.
In answer to your question, the ground level temperature was around +20 C and at 10,000, perhaps -10.
I don't see the where the reference to nonsense comes in. This is very similar to the type of situation to which DFC refers.
The difference in my case was that I was departing a VFR field into a low overcast with quite heavy rain and poor viz and had filed a flight plan where I would go IFR almost immediately. I could go to 13,000' for half an hour if I needed to but could also get back to non-icing conditions (lower level) as quickly as I could get up top. That is to say the rate of climb of the aircraft would not be a factor.
That's the way I planned it, that's the way it went. Didn't actually need to go to 13,000' or descend as 10,000' was riding through the tops and there was no further ice accretion.
The two main lessons are exercise the trim to it's full extent whenever you're going to fly at sub-zero temps (to get as much oil on it as possible), and if there is a fuel discrepancy (and there were three) find out exactly why and do something about it! I put it down to fuel seeping from one tank to another and due to the position of the fuel gauge (in the forward part of the main tank) when in flight, both phenomena which I had observed in the 350 or so hours which I had with this particular aircraft at the time.
You may not have anything to learn but these experiences are very relevant to the discussion.