IOWA CODE FOR BICYCLES

Bicycles as vehicles: 321.1
90. "Vehicle" means every device in, upon, or by which any person or property is or may be transported or drawn upon a highway. "Vehicle" does not include:
a. Any device moved by human power.
b. Any device used exclusively upon stationary rails or tracks.
c. Any integral part of a truck tractor or road tractor which is mounted on the frame of the truck tractor or road tractor immediately behind the cab and which may be used to transport persons and property but which cannot be drawn upon the highway by the truck tractor or another motor vehicle.
d. Any steering axle, dolly, auxiliary axle, or other integral part of another vehicle which in and of itself is incapable of commercially transporting any person or property but is used primarily to support another vehicle.

While Iowa law specifically excludes human powered devices from its definition of  a  "vehicle" it does grant the same rights and duties of a vehicle to bicycles under Section 321.234.

321.234 Bicycles, animals, or animal-drawn vehicles.
1. A person riding an animal or driving an animal drawing a vehicle upon a roadway is subject to the provisions of this chapter applicable to the driver of a vehicle, except those provisions of this chapter which by their nature can have no application.
2. A person, including a peace officer, riding a bicycle on the highway is subject to the provisions of this chapter and has all the rights and duties under this chapter applicable to the driver of a vehicle, except those provisions of this chapter which by their nature can have no application or those provisions for which specific exceptions have been set forth regarding police bicycles.
3. A person propelling a bicycle on the highway shall not ride other than upon or astride a permanent and regular seat attached to the bicycle.
4. A person shall not use a bicycle on the highway to carry more persons at one time than the number of persons for which the bicycle is designed and equipped.
5. This section does not apply to the use of a bicycle in a parade authorized by proper permit from local authorities.

321.236. Powers of local authorities.
Local authorities shall have no power to enact, enforce, or maintain any ordinance, rule or regulation in any way in conflict with, contrary to or inconsistent with the provisions of this chapter, and no such ordinance, rule or regulation of said local authorities heretofore or hereafter enacted shall have any force or effect, however the provisions of this chapter shall not be deemed to prevent local authorities with respect to streets and highways under their jurisdiction and within the reasonable exercise of the police power from:
10. Regulating the operation of bicycles and requiring the registration and licensing of the same, including the requirement of a registration fee. However, the regulations shall not conflict with the provisions of section 321.234.

Section 321.236 insures that the specific rights and duties granted to bicyles by state law cannot be revoked by local municipalities.   i.e: a local ordinance requiring bicycles to ride single file might be considered contrary to the right granted  in  321.275...

321.275 Operation of motorcycles and motorized bicycles.
1. General. The motor vehicle laws apply to the operators of motorcycles and motorized bicycles to the extent practically applicable.
2.
3.
4. Use of traffic lanes. Persons shall not operate motorcycles or motorized bicycles more than two abreast in a single lane. Except for persons operating such vehicles two abreast , a motor vehicle shall not be operated in a manner depriving a motorcycle or motorized bicycle operator of the full use of a lane. A motorcycle or motorized bicycle shall not be operated between lanes of traffic or between adjacent lines or rows of vehicles. The operator of a motorcycle or motorized bicycle shall not overtake and pass in the same lane occupied by the vehicle being overtaken unless the vehicle being overtaken is a motorcycle or motorized bicycle.

The above  statute does not specifically mention bicycles.  While you could argue that a bicycle has the same rights and duties as a motorized bicycle, it is probably safer to assume that the law does not specifically grant or deny the practice of riding two abreast to bicycles.

321.358. Stopping, standing or parking.
No person shall stop, stand, or park a vehicle, except when necessary to avoid conflict with other traffic or it compliance with the directions of a police office or traffic control device, in any of the following places:

1. On a sidewalk, except a bicycle may stop, stand, or park on a sidewalk if not prohibited by a local jurisdiction.

321.397. Lamps on bicycles.
Every bicycle shall be equipped with a lamp on the front exhibiting a white light, at the times specified in section 321.384, visible from a distance of at least three hundred feet to the front and with a lamp on the rear exhibiting , red light visible from a distance of three hundred feet to the rear; except that a red reflector may be used in lieu of , rear light. A peace officer riding a police bicycle is not required to use either front or rear lamps if duty so requires.

321.384 When lighted lamps required.
1. Every motor vehicle upon a highway within the state, at any time from sunset to sunrise, and at such other times when conditions such as fog, snow, sleet, or rain provide insufficient lighting to render clearly discernible persons and vehicles on the highway at a distance of five hundred feet ahead, shall display lighted head lamps as provided in section 321.415 , subject to exceptions with respect to parked vehicles as hereinafter stated.
2. Whenever requirement is hereinafter declared as to the distance from which certain lamps and devices shall render objects visible or within which such lamps or devices shall be visible, said provisions shall apply during the times stated in subsection 1 of this section upon a straight level unlighted highway under normal atmospheric conditions unless a different time or condition is expressly stated.

If you are riding anytime from sunset to sunrise or in conditions of limited visibility,  you must meet the above lighting requirements.   In the event of a collision,  some or all of the fault can be placed on the cyclist if you do not meet the minimum standards of the law.

321.434. Bicycle sirens or whistles.
A bicycle shall not be equipped with and a person shall not use upon a bicycle any siren or whistle. This section shall not apply to bicycles ridden by peace officers in the line of duty."