The Lumia 920 is designed to be used on 4G LTE, however it can use HSPA+, 3G, Edge, Wi-FI...
What I don't understand is why people want buy a Ferrari and only drive it a quarter of a mile before it gets put back in the garage until next summer. I get the gas is expensive but why did you buy it in the first place? When I bought an Xbox 360 for the first time I didn't have a way to get my high-speed internet connection on it. (Long story) I was missing out on some of the stronger selling points of the device. But I digress.
Should you be able to use your Wi-Fi when and where you want to? Sure. However, do the research before you buy the phone, you won't get burned. Make a list of pros and cons, including money you've invested into the current device you have and whatever apps you bought that you won't be able to use on the next device. I spent a lot of money on Android apps, mostly games but a few productivity apps that I can honestly say were quite helpful. Most of that functionality has been replaced with built-in apps on the Windows Phone 8 software. I ditched Evernote for OneNote and have not looked back. Native Office and Skydrive backup is pretty sweet, too. Does my phone have some quirks? Yes. I think a lot of phones have enough minor annoyances that they could make potential buyers hold off for a firmware update or another device completely.
I'm not a Windows Phone / Microsoft / Nokia loyalist. I bashed Windows Phone for the longest time. But, things change when you actually try it. Windows Phone 7 brought me to buying Windows 8 for my desktop, and eventually adding a line to get the Lumia 920. I went from a Android / Ubuntu set up to all Windows. The uniformity and convenience is wonderful. I have gained far more than I have lost.