I highly doubt that the USA will annex the entire CSA. They might annex parts of it and maybe give Cuba its independence ( or perhaps occupy it?). Out of curiosity, why do people think it'll be a USA and German Cold War. It could be a USA and Japanese Cold War.
Did some minor editing for you, since I guess you were in a hurry.
Granted, it's been a good while and I'm starting to reread the series, but I'm pretty sure that the US politicians (as seen from Laura's view point) have decided that after this war is over, the CSA will cease to be a political entity. Cuba might get independence as it's majority colored people, but the conCSA will be occupied. Texas, for example, won't be made independent as they've already restarted Houston as a signal of what is to come. Occupation is a sure thing, probably in more of the Soviet style of pacification than the OTL US in Germany. However, the states will be seated in Congress (as they were after WW1), even if they are sidelined/gagged/etc.
The idea for a German-US Cold War is mostly because Germany and America are the two greates powers (though no one will guess which is stronger), with Japan a distant fourth/fifth/sixth/etc., and after WW1 they struggled for dominance, each considering allying with their "partner's" former enemy. The Germans made calls to the CSA, and the US was softly approached by the French. However, since Britain couldn't be brought to one side or another as Britain hated both nations and was still a major power, when war came the US and Germany were still allied.
However, as I and a few other people have noted, this isn't as likely after WW2. The Germans aren't just going to sit on France and keep Britain out of Europe, and the US isn't just going to weaken the CSA more. This war is for dominance for the next century. The US plans to move back into the South despite knowing that the occupation will be the worst ever, and Germany will probably dismember France and take enough territory on it's east and west borders that France is forever gone as a power.
The trickier nations in defeat are Mexico, Russia, and Britain. Mexico and Russia will probably get off "lightly" in that rather than an occupation, they both lose territory. Western Russia will either be annexed by Germany, or turned into German puppet states. Mexico will be forced to give up at least Baja California (so the US never has to fight for it again) and possibly other parts, maybe pay an indemnity, and probably be forced to undergo democratic elections.
Britain isn't going to have a fun time after this. Empire? Forget Empire, it'll be lucky if it isn't split in two. Ireland is obvious, and so, it seems, are occupation troops. An atomic explosion over the royal palace or over London aren't too unlikely either. Though someone did point out the possibility that Britain could become the middleman between Germany and the USA.
However, Japan isn't as good a potential for a Cold War opponent. The Japanese dream in this TL is mastery of Asia and hopefully the Pacific, the first being more important than the other. And because Asia is so far away and the other powers have problems closer to home, they generally leave Japan to its doings. But while Japan still has a good surface navy, unless HT shifted some things around Japan is still going to occupy most of it's infant industry trying to hold onto it's empire, will still be militarist influenced, and still be economically poor compared to the US or Germany. Any atomics program, for example, will be a good decade later. And remember how they got caught funding Canadian rebels? The US here has a long memory, and wouldn't be uninclined to return the favor.
Japan might make the rank of top regional power in the same way Germany is for Europe and America is for America, but the multipolarity of the world keeps anyone from being a "true" Superpower.