Yes there bathrooms located all through the park
Restrooms are in the regular park, as was mentioned, beforr you go into the Peace Gardens.
Restrooms are locked in the winter
Yes
The restrooms are on the north side by the entrance to the regular park. There are none in the international peace gardens themselves. However they may be closed, they were on my last visit last month.
I spend 20 mins and find no restroom, so I'm gonna drive somewhere and come back.
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