Not sure. I suggest you look on their website.
I see why this question was asked. The website says that the visitor center is closed from October. However, the website does contain the following statement: 'The parking area for the visitor's center is open year-round, and access is dependent upon snow accumulations during winter months'. During the summer, there was a shuttle bus from the visitor center up to the top of the butte. But if the parking is open, then my assumption is that you are free to hike up to the top.
I would check the website.
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