My S3 LTE can connect to my phone via Bluetooth and can fall back to cellular if I'm out of range of the phone, but I can't convince it to use WiFi at all. I tried deleting the WiFi network in my phone and re-adding (while paired with the watch via bluetooth) and I've tried turning wifi off and on on the phone. Nothing seems to work to train the watch about my network. If I disable bluetooth on my phone, and disable LTE on the watch, the watch just shows "Disconnected". I can't get it to try WiFi at all. It's frustrating because my house is large enough that I frequently go out of bluetooth range and rely on WiFi to keep the watch paired with the phone during the day. This has always just worked with my Series 0 and Series 2 watches.