Being a process kind of person, I'd go. Cottonwood Lakes is a great place recreate.
Generally, It is not he up which is that dangerous, it's the down and you have to make sure you don't go too high into conditions you are not prepared to handle. With that said, New Army Pass would be your insurance policy, it is broader thus less dangerous in less than optimum conditions.
When it snows in early October, the snow melts out in most places because there is not a lot of it in most places. Army Pass is mostly on a north wall; therefore, the snow will persist to some degree but will not be enough of it to make crampons and an axe effective tools.
Another advantage of New Army Pass is you get a better view of Langley and the various routes to it. If you feel blocked, you have the option of doing Cirque Peak.
If you plans change and you use NAP, I would travel through the S.F. of Cottonwood Creek drainage and South Fork Lakes and camp at the west end of Long Lake. This route will save you about 2 miles round trip.