It always amazes me who people will argue till they are blue in the face about something they have no personal experience of.
Just like many others on here I have mo personal hands on experience of using Hot or wam water for WFP, so all I can do is surmise what will be.
I am in the process of going the immersion heater route, initially to heat up the water over night so it will act like a storage heater...not that I have any intention of having it waste heat warming the back of the van...what a waste!!
My van tank will be heavily insulated and boxed in, The DI cannister, pump and so on incorporated too.
With a separate section of of boxed insulation for the hose reel and pole hose.
The plan is to pull out the hose reels and whatever prior to starting work close off its insulated housing from van tank.
Whilst working with hot water the hoses and so on should be fine as warm water will passing though them keeping everything in a working condition.
Overnight the water in the van tank should still be pretty warm (I hope) providing I've done a top job with insulating the tank, the immersion heater should not need turning on for anything like as long in a poorly insulated tank.
I'd be extremely disappointed if I open the back doors of the van in the morning to find it like a sauna

Its a cheap way of testing out the merits of hot water window cleaning.
If it feels like a good bet, then I'll be looking at the cost of a small generator that is capable of running at 3kw.
If that is too expensive I'd look at getting something along the lines of Peter Fogwill 's Hot water system, Primarily with the idea of heating the water in the van tank rather than as an on demand system.
All of the above might be changed at a moments notice too!
All I can do at the moment is surmise as best I can...
If, for a relatively small outlay I can work when I might otherwise not be able too then it will be money well spent.
If water in my tank doesn't freeze, hoses do no freeze, water jets don't ice up and the bristlles on the brush also remain unfrozen, then that will do as a minimum.
In future winters my van will be fully insulated, ditto my production unit at home...I'll be properly winter-proofed, and that alone will be a godsend all of its own, because...boy!...this winter has been one hassle after another and I don't want to go through this again in a hurry that's for sure.
So cold water only guys, don't dismiss out of hand what you know nothing about, without at least trying it out for yourselves first!
Ian