Barry,
Perhaps you are confusing 'grinding' with 'honing'. The first removes metal which will leave machined work with the same marks as the grind gives. Honing gives a finish that used to be achieved after the 'rough to size' was completed on the lathe and then transferred to a grinder. I suspect that you know this but I'm trying to clarify for those with less experience.
I think that BaronJ was thinking along these lines.- with a coarse and fine stone at each end of your project. Perhaps he'll comment.
Reminiscing, my late wife's tool kit has a normal fine-sh hand stone but she had a white Arkansas stone to finish off. Again, she had - and I have a collection of fine instruments which extra stones from horses' hooves and broken taps or whatever! It all may dated but most of our machines would not seem out of place.
About weather, we didn't have problems with freezing in winter as the outside toilets or thrones, received coal ash from the kitchen fire and were emptied by the midnight mechanics. Unquestionably, there was a certain stimulus for self improvement.
And a caveat not to eat yellow snow:hDe:. So consider a simple honing jig- there are numerous ones, Bradley, Goniostats and funny little chariots which run along an old fashioned oil stone.
Keep cool!
Norm.
