One thing we didn't get was how big the group size was for the specific load to begin with.
If the group size was "good" (sub-moa as an example) before then you can rule out a few things:
1) Powder, 5" at 100M is much more drastic than the few FPS the speed will vary cause of temperature
2) Primer, if the groupings were good prior then the primer will have negligible difference at the temps you identified
3) Temperature, even in cold temperatures we are talking about a +/- half-moa. 5 moa because of temperature is unrealistic. If it was temperature you would expect the contracting of the barrel to offset the velocity loss. My current competition rifle shoots a +0.25 moa cold bore not -0.25moa.
The things I would look for personally, in the most likely order:
1) Shooter or shooting form
2) Bad round/load/batch
3) Dirty barrel
4) Loose mounts, scope rings, stock
5) Damaged scope
In terms of aiming, you should always sight in your rifle at max power. The old adage "Aim small, miss small" applies. If you sight in at 3x your crosshair likely covers a large portion of your target which increases your variability. If you zoom in to max you will be working with a more refined area and can minimize the impact of your own shooting variance. Within the scope the point of impact should be the same regardless of where you are in your zoom. Ranging is a different story and non-FFP scopes must be at the specified ranging zoom in order to range properly (without conversion calculations).
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