It depends on the weather really - and when they pull the planks on the suspension bridge.
Another issue would be resupplying. Sunrise closes on the 12th of October for the road, Mowich isn't much farther behind. The ranger station at Sunrise is already closed. If you didn't mind risking bridges being gone and carrying your food you might be able to do it.
Snow wouldn't as huge of a risk as rain and ice would be.