Ponderomotive forces (PFs) induced in cold subwavelength plasmas by an externally applied electromagnetic wave are studied analytically. To this end, the plasma is modeled as a sphere with a radially varying permittivity, and the internal electric fields are calculated by solving the macroscopic Maxwell equations using an expansion in Debye potentials. It is found that the PF is directed opposite to the plasma density gradient, similarly to large-scale plasmas. In the case of a uniform density profile, a residual spherically symmetric compressive PF is found, suggesting possibilities for contactless ponderomotive manipulation of homogeneous subwavelength objects. The presence of a surface PF on discontinuous plasma boundaries is derived. This force is essential for a microscopic description of the radiation-plasma interaction consistent with momentum conservation. It is shown that the PF integrated over the plasma volume is equivalent to the radiation pressure exerted on the plasma by the incident wave. The concept of radiative acceleration of subwavelength plasmas, proposed earlier, is applied to ultracold plasmas. It is estimated that these plasmas may be accelerated to keV ion energies, resulting in a neutralized beam with a brightness comparable to that of current high-performance ion sources.