Inspired by the TV series
1864.
According to wikipedia, "When the Prusso-German army approached the 'Danevirke line', the estuaries and marshes that had been planned to support the flanks were frozen solid in a hard winter and the command of the Danish army disobeyed orders and ordered a full orderly retreat back north to 'the old Dybbøl' and its ill-prepared flank position. There is little doubt that the command of the army did not believe that they could successfully repulse a well-prepared German siege and consequent assault on the Dybbøl position, and assumed that the political level would let the army be evacuated by sea and then fight the war on the principles of the north-south axis strategy.
But the political level did not appreciate the gravity of the situation, insisting on maintaining military presence in Schleswig and at the same time refused more modest German demands of peace. Hence the army was ordered to defend the Dybbøl position 'to the last man', and consequently the siege of Dybbøl began."
With the Prussian victory at Dybbøl, the war was effectively over, and the Prussians eventually overran the entirety of continental Denmark before the armistice.
What if the Danish government had had an attack of common sense and allowed the Danish Army to evacuate Dybbøl before the Prussians arrived? With the Danish Army still intact and on the field, would there have been any noticeable difference in the war? Personally, I believe Denmark never had a chance against both Prussia and Austria.