acooper,
You admire your instructor because he's managed to write a few hours in his logbook. Apparently he spent more time writing than gaining judgement. A Cessna 172 is not approved for flight into known icing, period. 10,000 hours isn't worth much more than the last hour flown, and that one apparently includes some very unwise judgement, from your post. Hardly something worth admiration.
Known ice occurs any time that conditions exist that might produce ice, or any time it is reported or forecast.
Putting a Cessna 172 of all things into conditions conducive to the formation of ice, especially freezing rain, is stupid. Very, very stupid.
Your instructor had no business continuing the approach with ice on the airplane; he should have landed. Period. You suggested that the ice was 'only accumulating slowly,' which suggests that it's okay to go flying in ice. Not so. You don't have much performance margin to begin with in the 172, and no available excess power to speak of. You have an airframe with the aerodynamic efficiency of a pickup truck. Adding ice can do nothing but hurt, and certainly not help.
What happens when you have that ice you can't shed, but need to land, and have to go around? You're fine leven and then on the descent, but what about the climb? Bad time to find out, isn't it?
If you accumulate ice faster, if the rate of accumulation increases or the amount of freezing rain increases, does being five miles from the airport make you less dead than say 10 miles from the airport?
Flying a Cessna 172 in ice is a risk taking operation. Flying in clouds in the winter is flying in ice, period. Ice can form, and apparently, it did. Your instructor has no business taking that airplane into the ice or the clouds in that area this time of year.
You're right; no forecaster could have predicted the intensity of the freezing rain, and neither could your instructor. But that aside, he had no business going in the cloud in the first place, or taking a student there. Not only were his actions rash and stupid, but he set a very poor example for both the students on board. Hours mean nothing; don't frame admiration for someone because they claim more ink than you in their logbook. A lot of pilots out there are still alive at this point in their careers due to luck, rather than good judgment and skill. The judgement this pilot has used speaks volumes. I certainly wouldn't fly with him or her, and you probably shouldn't, either.