IMO, what's more important in sub-zero temperatures is not whether you are able to work but consideration for any slip hazard you are going to cause!! If you haven't got the sense to acknowledge this then you shouldn't be out splashing water all over the place!
In general, skip doors or cloth them, then there's no issue.
Absolutely! With common sense you aint gonna course no slip hazards.
And the path all way round the house?
Are you for real with this or just looking for objections on going out? Or do you splash/spray water completely every where?
The huge majority of my work do not have their pathways or driveways butted against the very edge of their house. The majority have a border and if not, they have a drain away.
The vast majority of the water from upstairs windows fall onto the wall directly under the sill towards the downstairs windows.
Same for the downstairs or if not it falls/sweeps into the garden etc below.
Failing that and you get water everywhere and youn deem it a risk then carry rock salt with you and nip to van and bring some out.