Ordinary (mountain) bike tires hold pretty well in these conditions. You don't need snow chains. These guys are experienced and have biked stuff harder than Kredarica in snow seems to some. On the bike they're as safe as some of you on two ice axes (or one, depending on practice) and crampons or microspikes

That it's TNP and forbidden there is another story... with us it's easier to ban things than to regulate them.