Flying in rain does not usually have any possibility of icing.
Oooo, I've had rain turn into sticking freezing rain in flight, and that happens fast! If it's raining, and around +1C or so, watch out! I once flew into visible rain near freezing, and in addition to the windshield icing right over in an instant, the engine also stopped near instantly. I pulled carb heat, and it sprang to life. It was not carb ice (that takes a bit of time), but rather the air filter iced over instantly. The carb heat did not return the engine to running because of the heat, but rather the fact that it is also "alternate air", and the engine could breath the air from inside the cowl, and bypass the iced over air filter. I did a 180 right away, and it took a while for the windshield to clear, even with defog. The icing event, from entering the visible rain, to my turning 180 and exiting (including engine management) took less than a minute.
The older aircraft do have quite a safety margin, usually bigger compared to modern design, and we know this not by having cuddled pussy home cushions. Especially C172/C182/BE33/BE35 have been through quite serious and yes, sometimes believed to be dangerous, situations without harm.
These aircraft have built in safety margins for many things, like slight overspeed, over stress or over current. There is
no safety margin for flight in icing conditions - it has not been tested in non deiced types! It's not required to be tested for approval of non icing approved airplanes, so there is no formal knowledge of a safety margin for icing flying for these designs. That fact is probably the basis for the prohibition of flight in icing conditions for these types! So don't fly them in ice - at all! That's not hard to understand is it? The fact that someone on the internet can tell you to disregard the prohibition in the POH, and fly it into a "little ice" is just proof that pilots should take seriously what the POH says about the airplane, rather than comments on the internet!
No, if you pick up a little ice you have to be cautious, but not in fear.
No, you will be no test pilot, hundreds have been there and managed it
Gee, how much is a "little ice" on a 172, and what does "be cautious" mean while carrying that ice? Does being cautious mean that the pilot should realize that the aircraft will no longer perform the way the POH says it will? What's the new performance data or operating limitations while carrying ice? What's the new stall speed? Approach speed? Landing distance? Preferred flap selections?
No, blundering into ice contrary to limitations in the POH does not make you a test pilot. Test pilots fly airplanes with lots of planning, a defined configuration, and purposely gather data for a stated purpose. Maybe hundreds of non deiced airplanes have "managed" in ice. A whole lot have not managed, and crashed fatally also. How would a pilot know which outcome was ahead of them when carelessly entering icing conditions?
To the OP, it is wise to ask, make sure that the answers you read align with the more conservative understanding you gain from POH's and other sources you know to be authoritative! When you read an anonymous poster saying to disregard a caution, or prohibition, alarms should go off in your mind!