She sounds threatened, to me. Or perhaps she's the office "mean girl." There are people who do not like newcomers, and feel they're intruding on the office clique - real or imagined. My take on it is that, consciously or unconsiously, she wants to put you off-balance to ensure you understand that you're an outsider - and therefore don't expect to be welcomed with open arms. The only thing she could pounce on was the scarf - and she used it as her tool to chip at your self-confidence.
I suggest that you do not show that you take offense at this or any other snub that comes along. Continue to be friendly in a non-commital, professional way with her and all the staff. Continue to dress as you would and behave as you would. Be yourself - but do not rise to the bait.
Once your newness rubs off, and you've had the opportunity to assess the overall work environment and the personalities therein, I'm sure you will have a much better understanding of the office mentality and will be able to adjust your behavior to the situation and the person.
Of course, I could be way off base - and she's an unfortunate, social simpleton. Whatever she is, it will become more apparent as you settle in - and then you can deal with it accordingly.
Best of luck in your new job!