Diesel, of course not. Not in Canada. Honestly, I even leave my gasser idling while filling it when it's really cold. We are talking Canada cold, of course.
If I turn it off and it decides to go "GM Passlock Security" on me, we'll be stuck at the pump for 10 minutes. By then we will be cold and my wife will be grouchy.
We also refuel generators, pumps, quads and other power equipment while it's running. Gas and diesel. Sometimes with the clumsy mittens and those stupid ventless cans, fuel gets dumped all over their little motor, spark plug and all. Nothing has ever happened.
If I shut off my old wheeler long enough to fuel it, then I will need to take the heat gun to the heads again if I want it to start! Stupid cold weather.