The new free demo is out on Steam (and later, it will also be available on itch.io). It has reworked the second-level boss battle and added a completely new third level - the graveyard - with new weapons and enemy types. It's available here:
 https://store.steampowered.com/app/2244970/No_More_Snow/?utm_source=itchio

And you can have a sneak peak into what's coming in the full game here: