Yes, there is a register on the internet. Here is the link:
http://www.tc.gc.ca/aviation/activep...uicksearch.asp
All you gotta do, is to fill in the following:
Common Name: CESSNA
Model Name: 337
Leave the other fields open.
There are 83 337's active in Canada. In my view enough to warrant a fly-in somewhere picturesque (oh, the choices!) north of the border one day...just a suggestion (not a vote).
Oh, by the way, my 337 is a 1976, I guess that would make it a green dot, eh?