It is wrong, because lipids are formed with more saturated acyl chains. During adaptation to low temperatures, organisms may increase the production of lipids with more saturated acyl chains. So it's false.
As temperature decreases, the composition of membrane lipids (phospholipid fatty acids) is expected to become more unsaturated to maintain homeostasis. Although they differ in function, storage lipids (triacylglycerol fatty acids) are expected to respond to temperature changes in a similar manner.
When saturated fatty acids are compressed by a drop in temperature, they are compressed together to form a dense and fairly hard membrane. When unsaturated fatty acids are compressed, their terminal 'kinks' displace adjacent phospholipid molecules, maintaining membrane fluidity.
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