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If you use the expanding foam, and it is free to expand without pushing anything, it does make a great patch/glue material. You will want to cover it because it degrades under UV exposure, even a coat of paint would be enough. But, it is also damned hard to clean up and remove.
I think I'd rather take strips of plain cheesecloth (i.e. bandage cloth) a dunk them in plain beeswax, which seals and adheres very nicely, flexs a bit, and can easily be cleaned off in the spring. You can buy beeswax as "toilet seal rings" in any hardware store if it is't otherwise sold locally and cheaply, you don't need the food grade stuff for this. Think of this as biodegradable "fiberglass" done with less durable materials.
Duct tape isn't meant for long term exposure, I wouldn't trust it for the winter. Aluminum or stainless "gutter repair" tape is better for that, it can last close to forever but it also is going to cost more. And since it is a foil tape, it won't conform as easily as the waxed fabric.