Wi-Fi has never really been a battery killer. The thing that kills the battery is the mobile signal scanning through 2G, 3G or 4G if the signal is weak.
Case in point:
I live in Southern United Kingdom and my 920 easily lasts more than a day (heavy use) because the 4G signal is good and strong where I live. Last week I travelled to Northern Scotland for a week. As the signal is very weak up there, my phone was constantly scanning trying to get a good signal. As a result, I don't think I got more than 5 hours of very light use before having to charge.
Wi-Fi is your friend.... LOL!!!!