I did some looking to see what I could dig up on this interesting question. To start with, the most contemporary map of Lundy's Lane (also known as the Battle of Bridgewater) I found dates from 1816. It would appear that most other maps are based on this version.
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A second near contemporary British map can be found here:
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The Drummond Hill Church, as mentioned above, has been described as a red log building. The view found in Lossing, done in the 1860s, was used as the basis for a 1975 painting in the Niagara Falls Public Library collection.
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It is possible the wartime log church was rebuilt or it may have later been covered with white siding.
The same artist also did a painting of the Wilson Tavern. The source for this depiction is not provided, but it shows a single story building with a central doorway flanked by what appears to be one room on each side.
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The architecture of this painting of Wilson's Tavern is significant as a similar floorplan is found in the reproduction Laura Secord Homestead,
Front View: link
Rear View:
and in the postwar Laura Secord Cottage.
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Both of these buildings have two main rooms flanking a central entrance. The buildings also both have an upper half story with windows on the end walls. In terms of vernacular architecture these buildings strongly resemble the "advanced-center-passage hall-and parlour-house" from the Chesapeake Bay area (see Allen Noble, Wood Brick and Stone: The North American Settlement Landscape, Volume 1: Houses, 1984. pp. 49-51)
The last building of interest is the Buchner House built in 1799 adjacent to the Drummond Hill Church. The original house was a one-and-a-half stories "two bay" building. This is not very evident in modern views.
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But if you go to "6172 Buchner Place, Niagara Falls, ON" with Google Earth Street View and maneuver around to the back of the house the original structure can be better visualized. In contrast to the two Secord houses the Buchner House has a squarer footprint, an unbalanced facade and a single more-central chimney positon similar to the "one-and-a half New England cottage" found in New England and upstate New York. (Noble, pp.104-105)
The similarities to American vernacular houses are probably because Upper Canada (Ontario) was heavily settled by émigré Loyalists and they would have brought their housing practices along with them.