When a cottage in Ontario is owned by a limited liability corporation, formed in New York State and owned by US citizens, is the operating agreement still valid in Ontario?
Sure it is. If it was properly drafted in the states, it should be equally effective and valid in Ontario. Same for any contract, created in any province or state, applied to any other province or state.
The key here is “properly drafted.” At a minimum, it means the operating agreement—which lays out, for example, how the cottage is shared between the corporation members, whether it can be mortgaged or sold, and who contributes to expenses—has the elements of a valid contract. Your agreement must have been properly executed and properly signed by all parties involved when it was created. Contracts usually don’t fail because they don’t meet formal requirements but it can happen. If there’s reason to doubt your agreement’s validity, consult a lawyer.