It was a little icy in mid-August, so with a few storm that will inevitably occur by then, I would expect more ice. Depending on your comfort level with ice, it might be nothing to even think about. Talk to the climbing Rangers at Jenny Lake for a better report when you get there, and then consider that they may be telling you something not knowing the skill level you have. You might consider the Upper Exum if people report that as less icy.
Watch the Stettner Couloir for those big impressive slides.
I walked through up to 8" of snow and on 4' drifts hiking Peak 11,040'+ in the SW Absaroka on Sunday, 3 days after the last snow. I would guess the Tetons got in excess of 1' of snow out of those storms too. They looked pretty wintery on Friday.