The white-enameled WD-issue tin mug was standard issue for all of WW2....and it continued to be issued until stocks ran out, probably the 1950's.....
The brown-enameled variety was introduced in 1944, probably as part of the Far-East '44 pattern jungle kit, but issues did filter their way in limited use in the European theatre....
Post-WW2, the brown mug became commonplace.....but if you want an authentic WW2 appearance then go for white....and the more chipped and battered the better !!!
Original wartime WD tea mugs are rather hard to source today....but you can get very good replicas (made in China) that do an equally good job...:o)
I've seen lots of the green ones about...like most things that don't 'fit in' correctly I did what I often do and just assumed they were 'later' in a vague sort of way! ...Ian