I leave WFi and Cell turned on at all times. When I'm home reception bounces back and forth and the S3 never drains unusually fast. It's probably a good idea to follow your suggestion and turn off the wifi when I'm using my phone as a hot spot.
On a recent road trip I turned on the Hot Spot in my Galaxy S6 so my daughter could watch Netflix on her iPad. About 4 hours into the trip my Gear S3 gave a warning that it should be set for Power Saving and an hour later it was totally dead. What's up?