If you're injured and in an ambulance, worrying about your firearm should be the least of your concerns.
If Idaho (where you're at) is similar to Pennsylvania (where I'm at), the EMTs/Paramedics will, upon discovery of such, attempt to turn it over to an on-site law enforcement officer for safekeeping. If none is available, they will secure it within the ambulance and turn it over to the ER people along with the rest of your personal effects. The hospital should secure it just like any other valuables you might have on your person.
Now, if you're in New Jersey, be prepared to go straight from the hospital to a jail cell awaiting trial.