I occasionally use a bucket of warm water with Dawn dish soap & a long handled soft brush. I think I got the brush at an auto parts store or box box auto dept. then, after brushing I dump the water here & there on the bike. I try to use a conservative amount of soap so that rinsing with the same water is effective enough. ideally I'll bring the bike inside my basement to drip dry. then a day after when the chain is dry, I'll add some lube
sounds like you are riding on a paved multi use trail w occasional wet dirt stretches? I too prefer below freezing temps to keep that dirt firm & not soggy. in my area, we keep ice on shady trails almost all the way thru March. I tend to like gravel type roads rather than straight dirt which can be soft slow mud when saturated. & that makes for more washing. another minus
I like this kind of "hard pack", especially when dry. but even when wet, it isn't a mushy bog
I stay away from doing the drivetrain (too much), except "sometimes" & when I do, I use some other brushes. but for year-round removal of superficial but messy dirt & mud I use the long handled soft brush
but basically, this stuff is not staying on my bike