We can guess 1760-65 as a good date of the building of the Old House.
Actually, your guess is a good one
- but we don't need to guess because in Ep #605, while regaling Nicholas with the history of the house, Prof. Stokes reveals that the Old House was built in 1767 as a gift from Joshua to Naomi.
The Old House does reflect the Neoclassical or "Federal" style of architecture of the late 1700s, which borrowed from Greco-Roman designs.
As for the Old House reflecting the Neoclassical or the Classical Revival Style of architecture, that's partly true. The Spratt House (the real Old House) is actually in the Greek Revival Style and once again it's Stokes who refers to this (in Ep #475, during his hilarious first visit to the house when Barnabas wants to beg, borrow or buy an amulet for Dr. Lang to protect him from Cassandra's witchcraft) and that style grew out of Classical Revival. Greek Revival was its most popular between 1825 and 1860 - but Stokes conveniently covers that by saying that the Old House was constructed "before they got it right."
Perhaps there was a conscious decision to stay away from the Neoclassical style for the new manor and go for a French style. In real life Seaview Terrace was designed to resemble a French chateau. As a newly minted American, Joshua wouldn't want anything English in the design of the house. Since France was a valuable ally in the Revolution, it would make sense he would ape the look of an old chateau.
Well, remember that the original backstory of Collinwood on the daytime DS was that Jeremiah built it for Josette, so the fact that it's in the style of a French chateau made perfect sense (though, most interestingly, the backstory in Art Wallace's Shadows on the Wall describes Collinwood as having been "designed in the style of an English Manor House"). And as I've posted before, once Seaview was already established as Collinwood, even though they subsequently changed the house's backstory, they couldn't very well switch to a completely different house.
Anyone who might like to get deeper into the whole what style of architecture would actually have been appropriate for Collinwood issue and who might have missed it the first time around might want to check out "My Dream Collinwood (or would we really want "purely American" 1790s architecture?)" via the link below:
...