Yes the trail is open. This is the month I went 2years ago. As for snow, it does snow occasionally in the month of Oct. Please be aware, if you are staying in Ouray though the town is VERY small and often most of it has already closed for the season in Oct.
No snow or ice carvings this time of year. You can see the lower falls from the Lower Box Falls Trail. The Upper Box Canyon Falls are a lot more spectacular but the Trail is quite a bit tougher.
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