https://skjalden.com/plant-dye-colors-in-the-viking-age/
Looks like a useful source. In general you want to be looking at 'natural dyes' from whatever geographical area your minis are supposed to be from.
By the looks of the colours in the above link and things I have seen in viking museums and the like, I think you can use a pretty broad range. The main thing I would focus on is the vibrancy; natural, unrefined dyes are not usually as bright and rich as modern ones, and the cloth itself that was being dyed wouldn't have been bleached white in the same way it would be today either. Keeping that in mind, I'd be mixing in a grey/tan paint into any bright colours to make them a bit more muted and realistc for the peroid.
Just my two pennies [: