Since a Nazir is not allowed to drink wine, is wine vinegar also prohibited to Nezirim?
Yes, see Bamidbar 6:3
ג מיין ושכר יזיר, חמץ יין וחמץ שכר לא ישתה
he shall abstain from wine and strong drink: he shall drink no vinegar of wine, or vinegar of strong drink (JPS 1917)
For elaboration, see Mishneh Torah Hilchos Nezirus Chapter 5.