It was the kind of troops they sent. Had they sent better acclimatized soldiers from Patagonia, the British might have a worse time trying to dislodge them. Instead, fearing a Chilean invasion of Patagonia, they sent conscripts from the warmer north to freeze, with predictable results.
It wasn't the acclimatisation (or lack thereof) that was the issue. It was (in no particular order):
1. The uselessness of the junior officers, who were - from top to bottom and side to side - useless and a disgrace.
2. The abysmal state of training of the soldiers. Under stress, one defaults to the level of training, and the soldiers wouldn't even have passed basic training in any semi-competent army.
3. The sheer passivity of the defence. Quite why, I have no idea, but the defence was incredibly passive, allowing the British to control the battles.
4. The astonishing lack of fieldcraft. In the prelude to the Battle for Mount Harriet, Royal Marine patrols were able to follow Argentine patrols making their way through minefields, hence learning safe pathways through. In the prelude to the same Battle, the lead elements of the Royal Marines discovered that the Argentine forces had only set a single line of sentries, with no-one watching the sentries. As a result, the sentries were removed and the Argentine defenders none the wiser.
5. Poor quality senior NCOs. The Argentine NCOs did a lot of shouting, but to very modest effect.
6. Lack of familiarity with what being in action means.
The British had the Scots and Welch Guards who were also not acclimatised, and they coped.