There are multiple discussions available on this site about cold weather ball selections.

In your buddy’s case, he might have a point that works for him. Being an X it may feel too hard when cold - particularly in the wrists and elbows. It is a lower spinning version of the X. With a lower club head speed due to layering and a ball speed drop with temps under 50-55 F, the V may play better.

I play the same ball as I notice the drop off in every ball type. Below 50 I just play for the joy of being on course, not trying to accomplish what I get at 70+ F.

James, most here will say play the same ball the year round. Titleist also recommends that for year round consistency. I have played both balls and settled on the Prov1 which I had used and was curious about the Prov1x left dash. A golf ball is a personal thing and if you feel that changing the ball in the summer/winter and it helps your game, then go for it. But I play my Prov1 the year round and just adjust my club selection for best results. You can do a ball comparison by clicking on balls above and the click on Prov1 and scroll down until you find COMPARE FIND MY GOLF BALL and CLICK on Prov1 and Prov1x left dash. Will give you idea of how they perform. Both balls perform well the year round. My two cents worth.

The way I see it, lots of factors can lead to that conclusion. First, Titleist recommends staying year-round with the ball the has been fit to your game. That said, many amateur players do switch out for winter. Even if the ball is no different, the swing speed can be affected by layered clothing. Wetter fairways will affect roll out. Cooler temperatures might make a ball feel harder when hit. Titleist (and tour pros) say to adjust your club selection for winter distances but if changing to another Titleist model gives you confidence and confidence leads to better swings, do what you feel is best for you.