On the Bayeaux Tapestry they are depicted in mail with conical helmets but this seems unlikely to me, similar to 15th Century images of longbowmen in full plate armour. Would they have been largely unarmoured given the expense of manufacturing mail in the 11th century?
Actually, if you look at the full tapestry, specifically panels 26-32, you'll see a number of unarmoured figures in the margins, while the armoured figures are all, unsurprisingly, surrounding the kings and other nobles. Their retinues were indeed armed and armoured very well, considering their position. The remaining soldiery, however, appear to be much more lightly armoured, and armed with spears, bows, and shields, and little else.