It depends on the tuning strategy. On a stock car it's load based so as temps cool, it can hit the load target using less boost because air density is increased. Some people prefer this method because it gives your car a "break" you could say in the winter since it's not being pushed so hard lol
Using boost targeting you can make more power when it's cold. For example, in the summer the turbo may be hitting 22psi. In the cold, only 17psi. You can target the boost so it always tries to hit 22psi. There is a limit to this since the turbo can only flow so much. So while you might be targeting 22psi, it may run out of flow at 20psi.. still more than 17psi tho! As George said, in the summer boost targeting is nice because it sets a cap on the boost. My car in the summer on JB1 would hit 27-28psi. Personally going to use boost targeting and cap it at 25psi in the summer.
This is where having a compressor map helps since you'd know the limits, but unfortunately we don't have one for these turbos