If previous Winter plans were an example of this trip, no one is going to brave any threat of weather.
With solid weather reports, I've gone with just a bivy on multiple Winter snow trips. Granted, I also went with just a bivy and a tarp and got dumped on, but we sorta ignored the storm warnings. I bet your Lunar Solo would be fine. If there is snow, you'll brush it off through the night as needed. Probably get a lot of condensation. It's just one night out, though.
You can rent snow shoes at Badger Pass, the portal to Dewey. But they suck. Some good MSR Denali snowshoes can be rented at REI or A16. If that's unavailable to you, maybe someone can pick em up and get reimbursed.
Temps probably won't drop below 15F, and will most likely be somewhere between there and 26F. Unless you generally run cold, you can get by with a lot less than a big puffy arctic jacket. Here, I'll prep a gear guide to put some of this in perspective.