Guardsman Pass is a seasonal road that typically closes in early November. Big Cottonwood Canyon is open year round. On October 21, you should be able to drive. But there's any bad weather that day, you should check locally before going up there. A few years ago, we drove Guardsman in September when it was rainy and cool in the valley. As we approached the top it was foggy and we had a hard time seeing the side of the narrow road. It was a white knuckle drive. So just be sure you know what the conditions are.
Thanks for the tip!
For sure it won't be closed. The road has been improved dramatically in the last few years. It's completely blacktopped all the way to the top on the Salt Lake City side. It's also improved on the Park City side and now has barriers along much of the top section now on that side. Fun drive.