Mt Medvednica in detail
In winter there's skiing at the Sljeme Ski Resort Sljeme, which has five slopes of varying difficulty.
It's unlikely you'll want to sleep on Medvednica with Zagreb so close, though several mountain huts are available, should you wish to overnight.
There are several mountain huts that offer home-cooked traditional Croatian dishes served in a rustic setting. These include Runolist, Puntijarka and Grafičar.