carb ice experience

I had one experience that suggests carb ice makes the mixture too rich.
It was in a Mooney Ranger, I flying a VOR approach, pulled on the carb
heat knob and the damned thing just kept pulling out of the panel. It
broke! (Yes, I tested carb heat on the run up, it was fine.)

As luck would have it was to an uncontrolled airport in snow. The
second hand on the clock said look out and see the airport. I looked
and couldn't see a damned thing. Pushed the throttle in to fly the
miss, not much happened. I tried everything to get power back. Landing
light didn't help, raising the gear didn't, neither did prayers. The
one thing left to yank on was the mixture. I leaned it and the engine
began developing a little power, enough to limp to a nearby airport
with an ILS and get down. So leaning helped, which made me think the
mixture was too rich with carb ice.

By the way, if ever you want to overcontrol an airplane, fly down the
glide slope knowing you HAVE to get down, there wasn't enough power to
do anything else. I'm writing this story, so obviously I was able to
keep the needles crossed and got down. Those mountains in eastern PA
have been known to eat airplanes.

I remember that clearly even though it was 40 years ago. I wonder why?