I suppose you could paint it, if we also had transparent paint. Well, there are lacquers.
1. Rainwater needs to drain, even from gnarly little spaces like where the glass meets the wood. If the exterior wood is painted, then the paint needs to be maintained.
2. Interior humidity can and will condense onto the glass if the interior dewpoint is higher than the surface temperature. This can be hard to avoid in cold climates, especially if there are insulating window coverings over the glass. That condensation can drip onto the wood frame. (And, worse, could go through it into the wall cavity. It’s rather rare for the inside of a wall to be waterproofed and flashed like the outside ought to be.)
If I were building in a cold climate, I would stick with moisture-insensitive window frames. (Although aluminum, which can be quite pretty, has terrible thermal performance.)