There is plenty of room around the hut but there are also a lot peeps. My guess is you will not have to dig anything out.
As for steepness of the trail, it goes up at least 800'/mile to the hut and there are a few spots that can get puckerish with a heavy pack this time of year. I would not screw around through these sections. Put on the fangs and whip out the axe.
Overall, it is a fairly benign trip but there are few exposed sections.
