To me, it feels a bit unusual to say ?"Susan was walking with hands in pockets", but "Susan was walking, hands in pockets." seems perfectly fine.
English speaking people drop possessive adjectives and other pronouns all the time in their speech, but are much less likely to do so when writing things down. For someone learning English, it is probably better to keep them in, as it reduces ambiguity.
But yes, English does have a huge trend of clarifying many statements which could be perfectly clear from the context. But it's not a rule which must always be followed.
Another example: "The matron was standing there, staring at me, hands on her hips." Could be written as "The matron was standing there, staring, hands on hips." Whose hips her hands are on, is very obvious. Who she is staring at would have to be garned from context (i.e. the prior sentences).
So no, the possessive adjective is not strictly necessary, but until you intuitively understand when and where they can be dropped while retaining meaning, it is probably better to keep using them. But by all means, experiment.