Hi Arc,
Canadian law easily permits the operation of a private aircraft from private property, as long as it is safely done. Safely meaning that the distances and approaches are are suited to the aircraft and you're not flying right over someone else's home/business/livestock etc to accomplish your operation. New Brunswick is a beautiful province in which to fly though much of it's topography does not lend itself to purchasing property for your own runway. Your own runway is also a lot of work (ask me how I know!). There are some smal runways, though proportionatly not as many as elsewhere in Canada.
A floatplane on one of the rivers or lakes is another good choice for most of the year.
As for buying a plane, yup, they're for sale, all it takes is money! You will find a pleasing array of aircraft offered for sale from which to choose, though remind yourself that an aircraft offered for sale in Canada could be 2500 miles away from New Brunswick, and there are considerations in looking at it at the time of purchase, then getting it home!
I hope that helps, Pilot DAR