Where does “mud-” come from?

mud- (Proto-Germanic) comes from Proto-Indo-European mū- — fly, mosquito; fly, midge; lips, muzzle.

Ancestry of “mud-”, step by step

Step	Language	Word	Meaning
1	Proto-Indo-European	mū-	fly, mosquito; fly, midge; lips, muzzle

mud- — Etymology, Origin & Word History | Etymology Explorer