Let's not forget that Paul has stated on several occasions in the past that most of his songs are just made up.
We know, we know...but it's all in good fun.
(This reminds me of a high school poetry instructor I had who made us write poems on the spot during class. We would sometimes make up whatever we could think of just to get full credit, and we would laugh and roll our eyes at our instructor as he tried to read too deeply into our work... (rolleyes) ) However, I suppose if any of us were psychologists, we'd have fun picking apart Paul's lyrics to discover the "true" nature of his psyche...
I don't think we should be too suprised that many of Pauls songs appear "cold", as this does seem a dominant feature of Paul's personality. So many people have described as cold, distant, hard-to-know etc. I guess he's still just a traditional northern lad who keeps his real emotions on the inside, not on the sleeve.
I wonder if Paul's perceived coldness also has to do with the fact that he's been in the limelight for so many decades. I think he is wary of being taken advantage of by exploitative reporters, fans, and phony friends, and thus keeps people at an arm's length in order to protect himself.
Interestingly, though, I am in the middle of Geoff Emerick's book about the Beatles, and he describes Paul as being the most gregarious, warmest and friendliest out the four. However, I also recall that Robert Freeman described Paul as outgoing but reluctant to get too close.
Yet, in some ways, Paul's standoffishness make his songs a little more enticing. Since he doesn't like to be overly revealing in his lyrics, it leaves fans guessing if he had specific intentions when writing certain songs. (For instance, I've heard that "Riding to Vanity Fair" on "C&C" could be about his ex-wife Heather, but others have surmised that it could be about John...)