I know this seems like a simple question - but, I’m sure there will be a dozen good answers.
I got a bit of mud on my tire and pedals… also on my seat from dropping it (mud got down between plastic bumpers and seat material).
So, my first thought is just to take a hose to it and spray it off then leave it out in the sun to dry completely.
Then, I thought maybe I should wrap the hub in plastic just to keep from getting it soaked = rust?
It’s a Nimbus 26" in case that matters (ISIS hub).
Normally gravity and vibration does the job for me 
After some really muddy races last year, i hat to hose it, but normally i let the mud fall off from itself. When i need to take the muni in the trunk of my car, i just use an old shoe brush to brush the dry mud off.
I use a water hose and brush or rag to clean mine. As long as you don’t spray water directly at the bearings, it will be fine. Getting the bearings wet is fine though. Spraying directly at them with high pressure could push water, dirt and grit past the bearing seals. The seals will hold up fine otherwise.
About once a year I clean mine thoroughly with a cloth and WD40.
I hose KH26 muni off after almost every ride, because I keep it inside, probably moderate force jet, made with finger in the end of the hose. No problem with bearings after 2 years of that.
I just let the mud dry, then scrub it off with a brush (something like a nail brush), then if it needs it, I’ll wipe it down with a rag and some WD40 for a bit of shine. Bearings might get repacked every now and then but not too often as they don’t really need it
Water - soap and brush
rust
About 2 times a year I take the whole thing apart… actually we have a “party” in the basement and we all get to work – have to keep track of the parts with so many disassembled at the same time. Even have a 12" in there for the 4 year old. 
I tend to find surface rust on the outside of the bearings and it begins to show on the bearing caps. The screws that hold on the bear caps show surface rust as well.
I get out the “000” steel wool and get everything cleaned up…but it comes back even with things like WD-40, Lithium grease, and Silicone lubricant to help prevent it.
Is this typical?
I see videos of people riding in the ocean, mud, puddles… we’ve never done that, but seem to have this rust issue.
The bearings of my muni look the same and I’m 500 to 600 km away from the ocean. It’s perfectly normal.
Yep humidity and dust get between the bearing and the clamps and it takes ages to dry. Since the bearing doesn’t have a protective coat, it rusts (surface rust phew!). One thing you can do is put a thin layer of grease on the bearing before you put the uni back together, that will protect it. A bit.
+1 rusty bearings in all my Unicycles. Also I never wash/clean the Unicycles, I don’t mind the layers of mud on them (if anything I prefer it otherwise they look too clean!)
As long as you don’t get salt water on it, it will be fine, if you ever drop your uni in the sea, wash it of with fresh water immediately.
problem is, if you clean one, the others want to be cleaned as well. I you don’t they get grumpy and mutter among themselves for hours.