It is not possible to export the smart collection criteria.
This is one of about 12 bazillion reasons why one catalog is recommended and why multiple catalogs are considered inferior. If you combine your catalogs into one, then your existing smart collections will be there available for all of your photos.
Thanks for the prompt reply -
I thought as much, but thought I'd ask the experts first
Unfortunately, multiple catalogs are not an option for what I'm doing.
Note that you can import and export smart-collection definitions one at a time. Right-click the smart collection the source catalog and do Export Smart Collection Settings. In the destination catalog, right-click any collection in the Collections panel and do Import Smart Collection Settings. Unfortunately, you can't do more than one at a time.