Just quick reply cos gotta go & to a trim...
Rich pasture, muddy/soft environs are even more problematic to donks as to horses. They are really desert animals. You're already aware of the dangers of rich pasture obviously, which is great. Be aware that sugars build in grass during daylight hours, so it's safer to allow them night/early morning grazing & restrict them in the arvo where possible. Make sure they are getting low grade/low sugar hay, to reduce their grazing and make sure they aren't getting fat.
As for signs of laminitis, early signs may be subtle & go unrecognised, so it's important to manage to avoid it, rather than waiting to see what may. Signs such as hoof changes, stance, etc, mean the 'disease' has already progressed to a chronic & generally severe stage.
Loss of hair is likely mudfever. This is generally a fungal thing & you can reduce susceptibility by ensuring the donks are adequately supplemented for well balanced nutrition & their diet is low sugar/carbs.