Unfortunately, the fashion among Egyptian officers seems to have been to mostly wear the blue winter uniform, whatever the time of year. There seems to have been no strict policy of enforcing seasonal wear. British officers in Egyptian service would likely be a law unto themselves in the field, too, so the fact it was winter doesn't really help us, I fear. I'd be tempted to use the colour scheme from the Mike Snook book. It's the outfit that the Perry figure seems to be wearing, and you can't really rule out the possibility that he wore the same one as before, unless anybody has better info. It was only a few weeks later.
The nearest to a Sudanese winter I have ever been was Upper Egypt in January. Just about the coldest part of the year there. The locals were complaining of the cold and wearing sweaters, this boy from northern Europe had never felt hotter (it was pretty chilly at night, though).