According to Livy's account of the Battle of Trebia and the aftermath, some methods for preventing/treating hypothermia seem to include fires, blankets, moving about, and applying oil to the limbs. (Note that the 'hypothermia' I've identified below is just described as frigus or frigora -- 'cold, chill' -- by Livy. But it sounds severe and deadly.)

It happened to be the season of winter, a snowstorm was raging, and the district, situated between the Alps and the Apennines, was rendered especially cold by the vicinity of rivers and marshes. To make matters worse, men and horses alike had been hurriedly sent forward, without any food, without any protection against the cold, so they had no heat in them and the chilling blasts from the river made the cold still more severe as they approached it in their pursuit of the Numidians. But when they entered the water which had been swollen by the night's rain and was then breast high, their limbs became stiff with cold, and when they emerged on the other side they had hardly strength to hold their weapons; they began to grow faint from fatigue and as the day wore on, from hunger.

Hannibal's men, meanwhile, had made fires in front of their tents, oil had been distributed amongst the maniples for them to make their joints and limbs supple and they had time for an ample repast. When it was announced that the enemy had crossed the river they took their arms, feeling alert and active in mind and body, and marched to battle.

[An account of the battle]

The driving sleet and the intolerable cold caused the death of many men and baggage animals, and nearly all the elephants perished. The Carthaginians stopped their pursuit at the banks of the Trebia and returned to their camp so benumbed with cold that they hardly felt any joy in their victory. In the night the men who had guarded the camp, and the rest of the soldiers, mostly wounded, crossed the Trebia on rafts without any interference from the Carthaginians, either because the roaring of the storm prevented them from hearing or because they were unable to move through weariness and wounds and pretended that they heard nothing.

[Some more history...]

The soldiers rested whilst the intolerable cold lasted; it did not, however, last long, and at the first doubtful indications of spring Hannibal left his winter quarters for Etruria with the intention of inducing that nation to join forces with him, either voluntarily or under compulsion. During his passage of the Apennines he was overtaken by a storm of such severity as almost to surpass the horrors of the Alps. The rain was driven by the wind straight into the men's faces, and either they had to drop their weapons or if they tried to struggle against the hurricane it caught them and dashed them to the ground, so they came to a halt. Then they found that it was stopping their respiration so that they could not breathe, and they sat down for a short time with their backs to the wind. The heavens began to reverberate with terrific roar, and amidst the awful din lightning flashed and quivered. Sight and sound alike paralysed them with terror. At last, as the force of the gale increased owing to the rain having ceased, they saw that there was nothing for it but to pitch their camp on the ground where they had been caught by the storm. Now all their labour had to begin over again, for they could neither unroll anything nor fix anything, whatever was fixed did not stand, the wind tore everything into shreds and carried it off. Soon the moisture in the upper air above the cold mountain peaks froze and discharged such a shower of snow and hail that the men, giving up all further attempts, lay down as best they could, buried beneath their coverings rather than protected by them. This was followed by such intense cold that when any one attempted to rise out of that pitiable crowd of prostrate men and beasts it was a long time before he could get up, for his muscles being cramped and stiff with cold, he could hardly bend his limbs. At length, by exercising their arms and legs, they were able to move about, and began to recover their spirits; here and there fires were lighted, and those who were most helpless turned to their colleagues for help. They remained on that spot for two days like a force blockaded; many men and animals perished; of the elephants which survived the battle of the Trebia they lost seven.