I've never wrecked a pump trying to make it shove cold oil out onto the bar, but i have screwed up chains and turned bars blue...
In my area, and I suppose anywhere that the weather gets pretty cold you can get winter and summer bar oil. Summer oil is almost like STP, winter oil is more like tranny fluid or hydraulic oil with a little tacky goo in it. All I ever use now is the winter grade, mostly because it is a little cheaper. No problems with it.
I never substitute drain oil, 10W/40, or Mazola for bar oil. A long time ago, I used drain oil. Bad choice. It's pretty easy to find bar oil around here for $3 a gallon, even less if you keep your eyes open. Pretty hard to beat that price with anything else.