This morning, Barr Trail was 99% dry up to the "Half mile to Barr Camp" sign. The last half mile had significant stretches where the trail was snow packed, but they weren't a problem in any footwear. There were plenty of people hiking and running up and down. Who knows what tomorrow's storm will bring, but I'm guessing the new snow will mostly melt by mid-week.
Not sure about the Ruxton Creek section, as I went up and down the Incline and then joined onto Barr, but that might be closed for a while.