The road to the trailhead is completely dry, as is the trail up to treeline... after treeline there are some snow patches that are firm and icy in the morning and soft and wet in the afternoon. The snow is avoidable in some spots, but not really in others. Above treeline, the majority of the trail is a stream, so plan footwear accordingly. We didn't need/use traction. There was no snow on the route once you gain the S Arapaho/Old Baldy ridge that overlooks Arapaho Glacier.
The route from S to N Arapaho is 95% clear of snow... there are a couple patches, at times blocking the standard route, but they're avoidable using thoughtful alternate route finding. The summits are dry.