There is nothing special about synthetic motor oil, use it as you would any other oil.
I've begun using 0w20 Mobile 1 synthetic as a gun lube. It seems to resist thickening up in cold weather better than other oils. Oil may not be overly important to use in a bolt action rifle but it can be important with semiauto shotgun as some do not like to be run dry. The 0 weight rating keeps it viscosity well below zero so far. As I tend to have a quart or two in the truck emergency box, it is always around if I need it.
I have a fair bit of "gun specific" oil around but the light weight synthetic motor oil seems to be at least as good as well as being much cheaper.
Yes, there is something special about it. It does not freeze up nearly as easily as anything with standard petroleum. I have used Amsoil synthetic on many things and use it exclusively in my engines-for many years. Yes, 0w-20, or any other thin viscosity synthetic will be superior to petroleum.
