I just took my uni on my first muni ride and there was mud everywhere. Now I’m home and my uni is covered in mud. I have a '05 KH/Onza hub and crankset w/ Wellgo pedals. I took the frame off and wiped down the outside of the bearings. Tons of mud came off but a lot off grease came off with it. Should I grease up the bearings? Is there more I should do to the bearings? Are there other parts of my uni that I should clean?
Unless your bearings feel gritty or won’t turn, just wipe everything down, put a little grease on the metal surfaces of the bearings to counteract rust, put it back together, and go ride!
The main thing about a MUni is to get it dirty and have fun doing it. Bearings are cheap and easy to replace.
When I was riding off-road a lot I was always too tired afterwards to do a lot of uni cleaning. That’s probably the ideal situation 
I just use a utility brush to brush off the mud. Then I let what is left dry and then go over it with the brush again. Don’t get too fussy about getting all the dirt off. I just get enough of the mud off so it doesn’t make a mess in my car and then get enough of the dried mud off so it doesn’t make a mess at home.
Don’t wash it with a power sprayer. You’ll get water forced into places where it shouldn’t be and you’ll wash away grease. Don’t bother with washing it off with a low pressure hose either, no need. Just brush off the mud.
If you were just wiping the exterior and some grease came off then that’s fine. Probably just grease that had oozed out during assembly. If you’re taking things apart and wiping away grease then you’re probably wiping away grease that is supposed to be there.
A dirty muni is a happy muni.
If you ever ride through alot of water, or in the snow/rain, rinse your muni off in the shower to prevent rust. then just lighty pat it down with a towel.