Yes, there are many other expressions like this one, there are not always specific idioms, it’s also a valid structure where a nominal group is used with an adverbial meaning. A few examples coming to mind :

Partir la fleur au fusil (specific idiom)

Travailler les yeux baissés (I just composed this one, it’s not a specific expression)

Mâcher la bouche ouverte (unspecific, although probably used quite often)

You can see that for each of these examples, the preposition "avec" that you expected is not only absent, it would be redundant and may sound odd to some.