Big Dogs into Canada
This is a subject that I dealt with many times at the manufacturing company. Here are the broad strokes:
The rulebook says once a motorcycle has been issued a US or Canadian MSO (Manufacturer Statement of Origin) by the manufacturer, it can not be converted to the other. The MSO is the paperwork that later becomes the title on a new vehicle. However, there are (or were) loopholes in Canadian import law that allowed people and dealers to import US bikes (ex. Truckloads of Ironhorse bikes were being shipped up north of Alberta to an RV dealer before Ironhorse closed). There is only one guy can that help you find these loopholes. His name is Terry O'Brian with CCC Imports.
37 Hurst Drive
Barrie, ON L4N 9K6
(705) 719-2780
Be prepared to spend a little money. You will likely have to perform the same modifications to the bike as Big Dog did at the factory. These modifications include:
MPH to KMH Speedo (the new retrofit speedo will work)
Dual Rear Signals/brakelights/running lights (Requires brackets)
Dual Front Signals
Canada VIN Label
Depending on the model, it is likely that BDM Performance Products has most of the parts you need. The only item I see that may be a challenge is the 4-light module and harness needed for the rear lights. We may be able to make that for you. Let me know what you decide to do and I can dig into it further if you want.
The only other way I have seen people bring them across the border is to import them in pieces and register them as a "Home-built." I would discourage this approach because the border patrol agents are familiar with the Big Dogs and are wise to this approach.