Is it safe to keep iPhone's Hotspot on? I want to keep my laptop tethered to my phone's connection and was wondering if it is safe to keep emitting the personal hotspot wifi signal all day and anywhere I go (underground station, work, busy streets etc). Or would that have a risk of intrusion ?

My personal hotspot is password protected.
If you've password protected the network, the only worry you should have is battery life on the phone providing the hotspot.  You could also use a password with more entropy bits, but which is easier to remember. I would hazard a guess that not many folks are actively trying to crack random personal hotspots on the tube, walking around the park, grabbing an eel pie, or whatnot. I would suggest that if you remain concerned about it, just turn it off! You will certainly be saving some battery power and not zapping your gonads with wifi radiation, especially if you carry your phone in a pants pocket.