I know in 'medieval europe' the Miller as a thing. So Middle Iron Age yes. Early Iron Age though?
To be honest I'm more inclined to say the ancients had water powered things than to say they didn't. However, it would be a research challenge to find or not-find evidence of it.
Heck, the Babylonians had water gardens and the Eygptians seasonal irrigation troughs along the Nile. As for early iron age Finland, this I am not sure of.
A big factor is the finding of useful drops. In this regards I would think Finland with its Mountains, Cliffs and Hills would be likely to have them. Now, that is not necessarily going to be good places to farm.