We show the effects of a time-invariant magnetic field on the physical structure and magnetic properties of a colloid comprising 44 nm diameter magnetite magnetic nanoparticles, with a 24 nm dextran shell, in water. Structural ordering in this colloid parallel to the magnetic field occurs simultaneously with the onset of a colloidal uniaxial anisotropy. Further increases in the applied magnetic field cause the nanoparticles to order perpendicular to the field, producing unexpected colloidal unidirectional and trigonal anisotropies. This magnetic behavior is distinct from the cubic magnetocrystalline anisotropy of the magnetite and has its origins in the magnetic interactions among the mobile nanoparticles within the colloid. Specifically, these field-induced anisotropies and colloidal rearrangements result from the delicate balance between the magnetostatic and steric forces between magnetic nanoparticles. These magnetic and structural rearrangements are anticipated to influence applications that rely upon time-dependent relaxation of the magnetic colloids and fluid viscosity, such as magnetic hyperthermia and shock absorption.