Linda at Handcrafted History says it best in her blog post on the Viking Woman's Coat, "The existence of an open coat for women during the viking age is not a sure thing. We don’t know enough about the viking woman outfit to say for sure that this was what it looked like, or that they even were a thing. Why are they so popular in the reenactment world? They are practical for the kind of reenactment we do! A coat is easily added or taken of as we move between cold outdoors to heated housing, and excellent to add to your viking summer outfit for those colder events, without having to make a completely new outfit." I highly recommend checking out her blog post if you want a great tutorial on how to make this coat.
The other layers of this outfit are, like a lot of recreations of earlier period clothing, based on a handful of finds, scraps of fabric, and written descriptions. This outfit consists of:
Turnshoes (purchased)
Wool twill knee hose
A linen t-tunic style undergarment
A wool t-tunic style dress
A plainwoven belt (purchased)
A herringbone wool coat lined in silk and finished with a thrifted fox fur collar
Wool mittens (modern purchase, eventually I'll swap these out for properly nalbound mittens)