Today we went to VP from Stahovica past Primož. We avoided Pasje pečine via the upper path which goes about 50m higher and soon rejoins the path (bypass costs 5 or 10 min), the one over Pasje pečine. Both paths are already real highways two days after snowing (as you see on tol's pics), the one over Pasje pečine looks even more trodden. Where we went (upper path) crampons and ice axe definitely not necessary - path always in forest, nowhere crosses slope and not exposed. But crampons (with small teeth) come in handy if you don't want to slip on the path.
I was loaded today with ice axe and 12-point crampons, since first time and those few deca cost nothing. Next time probably exceptionally leave both at home.