Good grief...this is truly trawling the long lost depths of my brain
FFF the Saturated Adiabatic Lapse Rate and the Dry Adiabatic Lapse rates are different....thus the wet bulb temp and dry bulb temps on the ground are lapsed at two different rates...when you get to the altitude where those two temps are the same you get the theoretical cloud base. This is why the bigger the split the higher the cloudbase IF any cloud forms at all...which is not guaranteed.
In the case of your flight with only a 1 degree split you could be gauranteed IF there was any cloud the base would be quite low...as it was on the day...2500'
Now from memory dry adiabatic lapse rate is 2 degrees/1000' and saturated adiabatic lapse rate is 1.5 degree/1000'. Remember these are not exact but rounded numbers so dumb pilots can make calculations.
On the day in question;
0'............+3/+2
1000'.......+1/+.5
2000'.......-1/-1
So you can see the cloudbase was always going to be around 2000'
The ice problem is a seperate issue...you can see that the DALR hits 0 at 1500'...so in visible moisture you will experience icing...and by jove you did at 2000'...doesn't matter that you were in VMC...the rain started freezing on your airframe and unlike the jet you were not travelling at speeds sufficiently high for air friction to warm up the skin and alleviate that process.
I can't fecking believe I just pulled that ****e out of my head after 25 yrs
What happened to you was as close to a guaranteed outcome as aviation supplies....but a great bit of experience to tuck away