Hmm! You are from Australia so it figures that you wouldn't know how to scarf properly.
I noticed that the subject heading that you chose to use is "stripping". If you have to scarf, then you should never strip. The need for scarfing is indicative not only of foul weather but damned cold foul weather, probably with windy conditions, which could increase the windchill considerably. Oftentimes, such conditions occur during winter months but you should be experiencing summer weather conditions because you live in the southern hemisphere. Please, don't tell me that local temperatures dropped to below 25 C and now you are cold: that will just get me ranting about global warming.
As for scarfing...you start by wrapping the middle of the scarf around your neck so that both ends are hanging behind your back. You then bring each end up front so that the ends are hanging in the front. If done correctly, you will find a single layer of fabric covering the front of your neck. This wrap can be widened or narrowed according to confort levels. Each end of the scarf can then be left hanging outside your winter jacket or tucked in just above the zipper, which should be zipped up as much as possible. You would only tuck in your scarf ends in case of windy conditions, which could cause the scarf to be blown off your neck.
Now I know there are those of you who are probably itching to debate how to wrap the scarf in a so-called proper fashion. I am offering MY choices. Y'all can argue all ya want about what way is better.
I hope this helps.
Robert N(othing better to do) Pruden