Does all attic insulation from the 50's to 70's contain asbestos?

I plan on remodeling my cabin a little and am concerned whether or not to even attempt to do this due to possible asbestos in the insulation. The cabin has poor insulation ability as in doesn't retain heat very well and I believe it was built in the 50's or 60's. From what I remember it looked whitish and almost like wool or puffy material. Im going there this weekend and will look again and make sure what I am describing is accurate. I read online the Vermiculite can contain asbestos but its a pebble type material. I am almost positive it is not this but again im going to verify this, this weekend. I am going to take extra precautions and treat it like it has asbestos. I plan on removing an exterioir wall to and enclose the covered porch to give more room. any info will be great.