The starter coil can develop flat sections over time, especially if it's original. This situation doesn't like to crank whilst it's cold. If yours is original, I say bite the bullet and get a new starter. That said, I'd suspect the relay if you're not even hearing a click.
Winters were bad for the family '85 Accord.
I got a new shell, just need to stop driving the DX so I can work on it.
I've got a filter for my mouth, it just isn't a good one.