The Germans on the western front would have had some breathing room if they had all been captured or, worse, killed, but the allies would have reorganized and launched another attack, so not much would have changed. Really nothing. Assume for the moment that they are able to push to the coast and essentially encircle the whole northern half of the allied forces. Even in that case, Germany would be crushed by the Soviets.
The Germans will never survive past the summer of 45 in this world. It simply indicates that the iron curtain may have been moved slightly to the west. Very west, perhaps. In any case, it doesn't really matter.
It's unlikely that the final result would have been different even though a victory at the Battle of the Bulge would have probably threatened the majority of Belgian troops.
At this stage, Germany lacked the resources necessary for a protracted war, and the Battle of the Bulge depleted what little was left for German defense. They would still have had to contend with the 12th and 6th Army Groups in the south if they had been successful in pushing out of the Ardennes. They would also have had to decide whether to provide a significant defense in the south or try to close Allied forces in the north.
All things considered, though, it probably would have kept the Western front intact for the remainder of the winter. In addition to forcing NATO bases farther west and potentially stealing influence from more Central European states, the gains in what would have been Western Germany might have been much smaller, giving Eastern Germany much more control over Germany's economic output.
All of this, however, depends on the Western Allies' capacity to regain their momentum. There probably won't be any change if they can bounce back fast and possibly regain their losses in a short period of time. But if it kept them up for too long, Germany might have completely collapsed into a Soviet state, altering the Cold War's geopolitical results.