[David L.]

The difference between the two is that "to cover with" indicates that the object/thing is totally, or to a great extent, hidden by what is doing the 'covering'.
'to cover in' means something is all over the object, but not hiding it or there for the purpose of hiding the object.
It's easier to understand if we look at some actual sentences:

The boys were playing on the river bank, and came home covered in mud.
The dead body had been covered with leaves and bushes, and would not have been detected except for the trained sniffer dogs.

The back yard of the house was covered in a blanket of snow. The small wood pile was so covered with snow it was only by the end of a log still sticking out that he knew....

(A) It snowed so hard last night, my car was covered with snow.
(B) It snowed so hard last night, my car was covered in snow.
In (A) , my car would have been almost covered with so much snow I might have to do some digging out. In (B) my car had a lot of snow on the roof and the bonnet (hood).

She was so filthy rich that when she attended any function, she was covered in diamonds.
Whilst they waited for the police to arrive, they covered the corpse with a blanket.

The boy had a school yard fight and came home covered in bruises. There was a nasty looking graze on his leg, so his mother covered it with a bandage.