I have. over the last seven years since doing an Ottoman Scarf class with Alison Snepp, embroidered a number of scarves. Most of these were Raffal scarves, purchased as a follow-up to Alison's class. They are woven in India from Australian wool. The Raffal story is worth reading, a successful business established by one woman using the expertise she gained from working for the Australian Wool Board, utilising Australia's fine merino and the expertise of Indian weavers.
I am not sure if Raffal are still making perfectly plain scarves, but I had a couple left from my earlier purchase, and wanted to embroider one of them as a gift for a cousin who had kindly invited me to stay during my recent trip to England. I purchased scarves in colours that reflected the Australian bush, so chose a green one, sketched out some wattle branches and got to work.
It is a little tricky embroidering on these soft, open weave scarves. They resemble original Turkish bath towels - which is why Alison Snepp chose them for her original Ottoman scarf design. This means, however, you need to take great care in stitching, not to separate the fibres.
You also need to take care that the back is fairly neat - as scarves don't sit obligingly on one side. These considerations limit the stitches you can use.
I limited myself to French knots, stem stitch and fly stitch.
as I had done in the past, I added gold beads that sparkle. It's not too over-the-top but adds little glints as the scarf moves.
It worked - and is something that will get some use in England!