The mountain can be hiked without ever touching snow, but there are a few very easy snow crossings on the Silver Dollar trail, which is also very muddy. Beautiful hike, we only saw one other person. Wildflowers are in full bloom. Argentine appears unapproachable from the Argentine-Wilcox saddle unless you have snow equipment, but the Squaretop-Argentine saddle looked a little better. There is still plenty of snow on Argentine. Edwards looked to be completely dry.
We went up from Silver Dollar, which was perfect, and then descended the eastern face, which was very pretty until we hit the forests, which had a lot of dead and fallen trees. Unless you really know your way around the area I would avoid that route for a descent, it would have been very easy to get lost without GPS.
The road to the trailhead was very rutted and loose but was otherwise fine. High clearance is advisable. The area was swarming with people by noon.