All winter my garage is full of car muck. You know, the stuff that falls off the tires and mudflaps and fenders after having driven in the snow.
My way to get rid of it is to dump shovelfuls of show on it, spread it around, then shovel/squeegee out the whole mess.
How do you do it?
I can deal with the (ice boogers, snotsicles, fenderbergs) the same way you do, by using snow and then getting rid of the whole mess. The ice itself isn't a problem but it is usually full of salt which gradually ruins the concrete floor. Best to get the salt out before that happens.
Back in 1990 when my garage was new, my brother was storing his '73 Corvette in the garage, I put the door up using the house remote, walked out into the garage, got a few feet inside, smelled gas, and looked down at the floor...the tank on his car had leaked and spread about 10 gallons of gas on the floor!! I very carefully walked out, went into the house to shut off the power to the garage, went back out wearing rubber boots, then pushed my nearly new LTD outside, it was in the wintertime and I spread snow around the garage floor, it soaked up the gas and I moved it outside with a plastic blade shovel. Not sure what I would have done if the snow had not been handy.