It is an interesting idiom. It does come from boxing. When two fighters are boxing with their gloves on, they can casue more physical damage than with their gloves off. This is because the weight of the glove is added to the weight of your hand and it can inflict more internal damage.
If the boxers take their gloves off, the level of internal damage goes down, but the external damage goes up because their knuckles can cause cuts on the face which can lead to significant external blood loss.
Gloves on boxing therefore causes less visible damage, gloves off boxing is bloody and the spectators believe they are seeing much more damage.
So, saying that the "gloves are off" in any competition, including a political battle in Iowa, means a bloody encounter which looks, or sounds, ugly to anyone watching. The political fight in Iowa just got ugly with insults and "dirty tactics" becoming the format of the battle.