We studied the Battle of the Bulge in some detail when I attended the US Army Command and General Staff College. It offered some enduring lessons in some key areas which were useful to keep in mind when we were squared off to meet the Soviet hordes in Germany.
Intelligence was a big lesson. The allies had lulled themselves into complacency believing that the Germans could not launch another major offensive in the west. The US had basically screened the Ardennes, rather than defending the area in strength, believing that the hilly, forested terrain with few roads was a significant obstacle. The Germans achieved surprise at both the operational and tactical levels. The Germans had invaded through the Ardennes before in 1872, 1914 and 1914, so it wasn't unreasonable to expect that it could happen again. The 7 mile wide Losheim Gap was a dangerous route, which had been used each time before, but it was only screened by light cavalry patrols and became an area of major effort. A big lesson in operational security and constant intelligence gathering.
The German offensive was based on high speed operations led by panzer formations which moved on the few routes available and sought to achieve high speed penetrations into the allied rear. Movement was canalized to the few roads available and was vulnerable to interdiction at defiles thru high and forested areas and at key crossroads. American countermoves had to be directed at choking off these routes and holding road junctions, like the ones at St Vith, Mamedy and Bastogne. Every bit of delay imposed this way was gold. That's why the early fighting at St Vith and later holding of Bastogne was so critical. Soviet doctrine was based on continuous high tempo offensive operations along movement corridors which could be doctrinally predicted and template on the terrain so we drew the same conclusions in planning to defend against them.
Once the weather improved allied airpower was used to destroy German forces in contact and to interdict routes and reinforcements in the rear. This was a prelude to the Airland Battle doctrine which hit the street in 1980 and was based on deep attack to separate follow on Soviet echelons and destroy them while troops in contact fought their lead echelons.
The Bulge was an excellent illustration that the best way to handle an enemy penetration is to beef up and hold both shoulders securely to limit the width of the penetration and then allow the enemy to advance to some depth where he could be cut off and chewed up by attacks from the flanks and become isolated from his logistics and reinforcements. This is basically what Patton's Third army achieved when moving up from the south to relieve Bastogne. There were equally effective US attacks on the north side of the German bulge.
Logistics was a big lesson. The Germans had everything in the shop window and had weighted their armored formations, but they were basically road bound with a horse and wagon logistics system which was short on fuel and could be interdicted from the air. Its never good when your logistics plans for an attack are based on capturing enemy fuel supplies intact. Probably as many German tanks were neutralized by running out of gas than by being destroyed. As the battle developed US logistics continued to improve while German capacity diminished. Availability of arty ammo was and still is a big determinant.