Quite timely, given the recent weather: I have one short, but steep, climb to face everyday on my winter route. If it is icy, you aren't getting up a hill without "Bums in seats!" and on my fixed gear I am not ever getting up that hill without standing up, so there is nowt for it but a slippery walk.
Screw anyone's stupid rules for cycling. People who balk at the idea of walking up a hill are the type of people who are still cosy in bed when I'm walking up that hill, waiting until they get up and drive to work, because they only cycle at the weekend when it is sunny.