I have never seen any indication this area would be closed. It will be hard to navigate the side roads if it snows or has heavy rain.

You can check road status in this area here https://www.fs.usda.gov/detail/coconino/alerts-notices/?cid=stelprdb5339811 Closed or not, this area can get pretty soggy with snow and we've known one person who had to get pulled out.

There was no indication on signs about this area closing at any time. That being said, I would not be surprised if it became hard to navigate in the snow and rain of winter and I suppose they could gate it off.