I haven't been out of the area since the storm as the roads were abysmal on Sunday. I cant comment on the snow conditions at Starr King, given the weather pattern and temps close to freezing, the rain may or may not have eaten into the snow accumulation. I seriously doubt you need powder shoes as I expect the crust will be pretty heavy duty after a couple of cold nights and possible slightly warmer days later in the week with cold nights will further develop the crust. This trail get heavy use and expect there is probably a well established path already.
I can comment on parking situation at Starr King. The intent is that there is a summer parking area off a spur off private road that services a couple of houses in this area. The summer parking area was built at one point as hikers were routinely plugging access to the private homes. The individual that plows the road typically plows in the road to the spur. Folks with high clearance 4WD may be able to driveover the banking to the spur lot (then again they may not and will get to contribute to local economy by having to pay for a tow truck) At this point the official parking is at winter lot on the south side of RT 2, not along the road accessing the houses. The entrance to this winter lot is about 50 yards west of the road to the summer trailhead. Its field in the summer next to gray house. It is a seasonal lot and is lower than the highway and tends to turn into "skating rink" especially with the recent weather conditions. Its easy to pull in but not so easy to pull out onto RT 2. My preference is to park in plowed parking spaces just east of the Irving station on the south side of RT 2 . These parking spaces are used by the church on the north side of the road on Sundays and the town keeps them plowed. I try not to park at Irving as they are business that needs parking. I rarely see hikers parking at the scenic pull out that is east of the Starr King road. Odds are highly likely that if its a nice day, you will find plenty of cars parked along the road up to the summer lot inevitably blocking the homes along this way. Many folks rationalize that the homes are unoccupied in the winter and the owners will not mind, they forget about fire access which is probably why the road is plowed in the first place.