Depends on the mix, three parts sand to one part cement firmly placed on the glass and hot water wont touch it, if its been watered down with very little cement left then hot or cold will remove it, either way its full of grit and by brushing it off you risk scraping the glass, Nathans customers have found this out to their cost.
As for egg on upper window frames, well in twelve years on wfp Iv never had that problem so i cant say if it it helps or not.