This entire analysis presumes the standpoint of epic, not Orwellian Dystopia.

Battle of Yavin notwithstanding, Imperial Dominance in the galaxy is beyond question. Palpatine pursues the rebels because by creating a foe, he may subject significant portions of the Old Republic/Current Empire on the basis of fear of an unseen, poorly organized rebellion with just enough military power to disrupt the comfortable existence of any single system, but in general, not enough military threat to truly challenge for dominance. Palpatine's motivations are to maintain the standard of wealth he has earned, and the is only possible by engagement if a fake war against an ideology. It is so mind-boggling expensive to subjugate the galaxy, he requires huge taxes which can only be justified in the face of a significant threat. If public perception of the Rebels was that of a band of mostly harmless, ineffective ingrates, then Palpatine would not be able to levy the crippling taxes necessary to keep his Imperial Army/Navy funded. And allowing the destruction of the original Death Star allows Palpatine to continue to impress the need to funnel huge taxes to his friends in the Military Industrial complex to build another.

Couple this Orwellian Manipulation with the imperial dominance watering down its officer's military training. Given the strategic edge they have over every conceivable opponent, their doctrine shifts from carefully achieving victory to minimizing losses of high-value targets. And strategic thinking? Demonstrably non existent. Once you Realize the Rebels are at Hoth, a sensible Prince ala Machiavelli or Sun Tzu would do everything in his power to keep the Rebels at Hoth. Staying on a frozen wasteland will do nothing but deplete resources. There is no rebuilding on Hoth, there is no resupply; all there is comes down to wound-licking and frostbite. And in the face of a Jotenheimian hellscape, Hoth quickly destroys any positive morale to be had by the destruction of the Original Death Star at Yavin.

Vader is show to be a fairly daft fellow (cf Episodes 1-3), easily manipulated, impulsive and incapable of foresight. In essence, he is given the fool's errand by Palpatine to keep him busy, because questions of intellect aside, he is shown to be a mighty enough warrior to challenge Palpatine in a direct confrontation. As an axeman, Vader ranks highly, as a stratetician, he is very poor. Unfortunately, Palpatine can't really get rid of him either. There is no justification, nor any replacement which would serve to bolster up the fear. Remember, as fierce as Palpatine may be in combat, he weakens his imperial authority to be shown 'getting his hands dirty' from the throne. He's stuck with Vader.

In essence, Vader lost at Hoth because Palpatine set him up for failure. Vader is a figurehead general, and no more.

This entire analysis presumes the standpoint of epic, not Orwellian Dystopia.

Battle of Yavin notwithstanding, Imperial Dominance in the galaxy is beyond question. Palpatine pursues the rebels because by creating a foe, he may subject significant portions of the Old Republic/Current Empire on the basis of fear of an unseen, poorly organized rebellion with just enough military power to disrupt the comfortable existence of any single system, but in general, not enough military threat to truly challenge for dominance. Palpatine's motivations are to maintain the standard of wealth he has earned, and the is only possible by engagement is a fake war against an ideology. It is so mind-boggling expensive to subjugate the galaxy, he requires huge taxes which can only be justified in the face of a significant threat. If public perception of the Rebels was that of a band of mostly harmless, ineffective ingrates, then Palpatine would not be able to levy the crippling taxes necessary to keep his Imperial Army/Navy funded. And allowing the destruction of the original Death Star allows Palpatine to continue to impress the need to funnel huge taxes to his friends in the Military Industrial complex to build another.

Couple this Orwellian Manipulation with the imperial dominance watering down its officer's military training. Given the strategic edge they have over every conceivable opponent, their doctrine shifts from carefully achieving victory to minimizing losses of high-value targets. And strategic thinking? Demonstrably non existent. Once you Realize the Rebels are at Hoth, a sensible Prince ala Machiavelli or Sun Tzu would do everything in his power to keep the Rebels at Hoth. Staying on a frozen wasteland will do nothing but deplete resources. There is no rebuilding on Hoth, there is no resupply; all there is comes down to wound-licking and frostbite. And in the face of a Jotenheimian hellscape, Hoth quickly destroys any positive morale to be had by the destruction of the Original Death Star at Yavin.

Vader is show to be a fairly daft fellow (cf Episodes 1-3), easily manipulated, impulsive and incapable of foresight. In essence, he is given the fool's errand by Palpatine to keep him busy, because questions of intellect aside, he is shown to be a mighty enough warrior to challenge Palpatine in a direct confrontation. As an axeman, Vader ranks highly, as a stratetician, he is very poor. Unfortunately, Palpatine can't really get rid of him either. There is no justification, nor any replacement which would serve to bolster up the fear. Remember, as fierce as Palpatine may be in combat, he weakens his imperial authority to be shown 'getting his hands dirty' from the throne. He's stuck with Vader.

In essence, Vader lost at Hoth because Palpatine set him up for failure. Vader is a figurehead general, and no more.