Falling rain occurs from a relatively warm layer of air, lying above a cold sector. The precipitation becomes supercooled as it falls then finds your cold aircraft toodling along below as a freezing "nucleus".... nasty!
Yes, this I have encountered, and it is very bad. It is visible as you approach it though, as it is percipitation.
I have hit it twice, thinking it was only rain. On both occasions, the engine stopped within seconds, as the air filter ices over (alternate air fixes that adequately) and the winshield ices over (which takes much longer to get running again!)
You'll have enough time, and good motivation, to do a 180 and get out. The airplane will remain suitably safe to fly, as long as you're gentle. The airframe ice you pick up is clear, which is not a lift destroying as rime. Don't linger there though!
Nothing in the foregoing is an endorsement of flying into any kind of freezing percipitaion, or other form of icing conditions, unless completely equipped and qualified. It is simply a reassurance that doing so is not immediately fatal, if you get right out, and keep your head about you.
Three times I have been falling out of control, because of airframe ice (I eventually learned - it was just more than one lesson). Once in a C150 at night over the mountains as a pre student passenger (more than one lesson there!), Once in a Twin Otter over the south of France, on a nice August day (yup, lesson there too), and the third time flying a very new Cessna 303, which was fully serviceable, and fully deiced for known icing. It was the AD forbidding flight into icing, in that model aircraft, which had not been properly placarded, and was thus unknown to me. (lesson on placarding and AD compliance there). Each time luck exceeded skill and judgement, so I'm here writing. A dear friend did much less well, and told me (12 hours after the crash) that in his Piper Dakota (235HP), with full power, the best he could manage was 70 knots, as he decended at 2200 FPM. He hit the trees that way. Unforecast icing conditions between layers at night - he had not been attuned to slowly degrading performance, which had given him lots of warning. He survivied - that time...
If you can't see what you're flying into, don't fly VFR into it. Use extra caution near freezing, and at night (and over the south of France). If you have good visibilty, and no percipitation, use good judgement, but go and enjoy a nice winter flight!