I have discovered 17 places in Lincolnshire named "Cold Harbour", many of them are names of farms, houses or just a patch of land. I have seen many suggestions for the name, the most common is 'a place where a Roman building once stood'.
Unfortunately it is not as exciting as that; if we remove the 'H' from the second word we get Arbour, which some keen gardeners build to make a pleasant shelter to sit beneath on a warm sunny day.
Historically a Cold Arbour is a clump of trees, a ruined building or a depression in the land where travellers could get some shelter from the weather.
The image below is a map showing the location (blue tag) of a cold arbour at the junction of the High Dyke and A52 near Grantham. It's interesting that the public house was called the Blue Harbour, possibly owned by the same Lord of the Manor who owned the "Blue" inns in Grantham. See https://itsaboutlincoln.blogspot.com/2017/11/the-blue-inns-and-sign.html