In general, due to thermal expansion, materials will contract under colder temperatures and expand under hotter temperatures. This goes for the poles as well as the plastic fibers that make up the fabric of the tarp. Theoretical expansion/contraction is pretty simple for basic shapes like a block, cylinder, tube... I wouldn't claim to have any real knowledge for how this affects materials with complex geometry like a fabric woven from extremely thin/long fibers. I would assume though that the overall width of the tarp pulled taut would measure less in winter temps and more in summer temps. Likewise, the poles will be a little shorter in winter than they would in summer, by small amounts - fractions of an inch.
So it may not be that the tarp stretches less when it's cold - it's technically a "smaller" tarp when it's outside in the cold vs. when it's at ambient indoor temperatures.
As a winter tarp, it probably makes the most sense for the pole length to be sized correctly for the tarp when both are at cold temperatures, say 0*F.
No real help here... just some random musings...
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