Did you see that phrase as one single compound noun (ie He had some honk snot balls)?
"Snot" in BrE is the wet mucus stuff from your nose. If a child's nose is leaking the liquid clear/green stuff, then it is referred to as "snot".
I don't know if it's "honk" as a noun or a verb. If it's a verb then I imagine it's being used to describe the disgusting habit that some people have of holding one nostril shut with their fingers, and then expelling air and snot out of the other nostril onto the street at high speed.
In my opinion, it's not being used to describe any kind of spit, which is saliva and comes from the mouth. That doesn't fit with "snot".