I've often heard and read that Sherlock Holmes never wore a deerstalker cap, that it was an invention of the illustrators or film directors and so on. But in "Silver Blaze", the story with the incident of the dog in the night, Watson describes Holmes on the train to Tavistock "with his sharp, eager face framed in his flapped travelling cap..." So, perhaps it was not a great leap to a deerstalker, although that is a harder sort of hat, rather than a soft cap.
The new Sherlock TV series has made me revisit the stories with great pleasure. Is there any basis for making him out a modern man, or at least one ahead of his time? He certainly uses all the latest science available, at least if it is relevant to his interests. He has a subversive or transgressive streak and is heartless in his treatment of a female servant in Charles Augustus Milverton, in a similar way to Sherlock's treatment of the Irish PA in the TV series. And his (or Doyle's) language sometimes has a contemporary feel. I have already noted free play with ungradable adjectives, as in "very unique". Other usages which are now thought of as modern horrors are also in evidence, "past history", for example.