There is a 2nd mountain hut called "Chata Vileminka" on the czech south side but I could not find any relevant link on it... perhaps this one: http://www.vileminka.cz/
Perhaps you should also mention whether wild-camping is allowed or not on Snieznik
There are also caves in the valley south of the summit, on the Czech side. The most interesting is Patzelt Cave, named after a ranger who fell into an underground pond in there while walking through the forest. Bear in mind a visit can be dangerous as the: warnings by the entrance read