Esqueletos de referência:
Sim, eles podem equipar armas e armaduras.
O não inerentemente tem desvantagem com quaisquer armas ou armaduras.
Fonte: Monster Manual pg. 272
Animated Dead. Whatever sinister force awakens a skeleton infuses its bones with a dark vitality, adhering joint to joint and reassembling dismantled limbs. This energy motivates a skeleton to move and think in a rudimentary fashion, though only as a pale imitation of the way it behaved in life. An animated skeleton retains no connection to its past, although resurrecting a skeleton restores it body and soul, banishing the hateful undead spirit that empowers it. While most skeletons are the animated remains of dead humans and other humanoids, skeletal undead can be created from the bones of other creatures besides humanoids, giving rise to a host of terrifying and unique forms.
Porção que se aplica diretamente à questão, a ênfase em bits importantes é minha:
Obedient Servants. Skeletons raised by spell are bound to the will of their creator. They follow orders to the letter, never questioning the tasks their masters give them, regardless of the consequences. Because of their literal interpretation of commands and unwavering obedience, skeletons adapt poorly to changing circumstances. They can't read, speak, emote, or communicate in any way except to nod, shake their heads, or point. Still, skeletons are able to accomplish a variety of relatively complex tasks. A skeleton can fight with weapons and wear armor, can load and fire a catapult or ttebuchet, scale a siege ladder, form a shield wall, or dump boiling oil. However, it must receive careful instructions explaining how such tasks are accomplished. Although they lack the intellect they possessed in life, skeletons aren't mindless. Rather than break its limbs attempting to batter its way through an iron door, a skeleton tries the handle first. If that doesn't work, it searches for another way through or around the obstacle.
Zumbis de referência:
Sim, existe uma referência direta às armas. Não, eles não estão em desvantagem.
Fonte: Monster Manual pg. 315, sob o parágrafo Mindless Soldiers .
A zombie armed with a weapon uses it, but the zombie won't retrieve a dropped weapon or other tool until told to do so.