Bill Smith, there's a lot of good discussion here, but your question posed is very very type specific.
Here is ONE of many reasons why Vr may decrease whilst V2 increases on a cold day. There are others, which may have the opposite effect.
One of the more critical performance limitations to be considered in aircraft certification is the capability to accelerate from V1 (on the runway) to V2 (at 35 ft above the runway) within the Takeoff distance available (TODA). At high temperatures (and therefore lower thrust) this can be very limiting, particularly for a 2 engined aircraft with one engine inoperative. It's necessary to shorten the gap between Vr and V2 as much as possible in these circumstances to accomplish this acceleration. In the worst case, V1 will be at the highest (causing the aircraft to be accelerate-stop limited) and V2 at V2 min, yielding the lowest 2nd segment climb gradient.
As the temperature decreases, thrust increases, making the Vr to V2 acceleration less limiting, and the certifying Performance Engineer can then avail him/herself of using a lower V1 (allowing an increased accelerate-stop limit weight), and a higher V2 (allowing an increase in 2nd segment climb limit weight).
This increasing Vr to V2 delta can widen as temperature decreases, down to the temperature where the engine becomes Flat Rated, whereafter little is gained from manipulating the numbers further (a little, but not a lot).
Again, I say that it's very very type specific, some manufacturers adopt one simplified schedule of speeds, and adjust the performance penalties around that, rather than adjusting the speeds within the approved limits to gain the optimum performance.
Regards,
Old Smokey