I would recommend hiking boots, or boots in general. Trails can be muddy or icy in winter.
Depends on the weather that day. I would strongly recommend something else other than running or tennis shoes. Great place to explore any time of year though
Probably depends on the day, but I am heading there today with hiking shoes - this is year-round footwear for me there. I went there two weeks ago as well, same. Just note that it is typically windy, so if it is a cold day, the wind chill will be more noticeable.
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