The magnetic properties of the axion insulator candidate ${\mathrm{EuSn}}_{2}{\mathrm{P}}_{2}$ are comprehensively investigated. Under an applied external field, the antiferromagnetic phase below 30 K is driven to a forced ferromagnetic state. The yielded Rhodes-Wolfarth ratio (RWR) is equal to 1.13 (1.12) with $H//ab$ $(H//c)$, indicating the forced ferromagnetism in ${\mathrm{EuSn}}_{2}{\mathrm{P}}_{2}$ is weak itinerant. A large magnetocrystalline anisotropy with ${K}_{u}=521$ $\mathrm{kJ}/{\mathrm{m}}^{3}$ at 2 K is evaluated. Analysis on the critical behavior generates a set of critical exponents $\ensuremath{\beta}=0.281(2)$ with ${T}_{C}=30.2(1)$ K, $\ensuremath{\gamma}=0.77(3)$ with ${T}_{C}=30.1(1)$ K, and $\ensuremath{\delta}=3.76(4)$ at ${T}_{C}=30$ K, exhibiting a three-dimensional critical behavior. A phase diagram of $H$ versus $T$ is established, where a tricritical point at temperature and field of (30 K, 16.7 kOe) is determined on the boundaries of the paramagnetic, antiferromagnetic, and forced ferromagnetic states. In addition, the magnetic entropy change exhibits anisotropic behavior. The maximal value of the magnetic entropy $\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{M}^{\text{max}}$ reaches 7.36 (6.41) J ${\mathrm{kg}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ with a magnetic field change of 50 kOe in $H//ab$ $(H//c)$, which is comparable with that of well-known materials suitable for magnetic refrigeration with second-order ferromagnetic transitions. The plots of $\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{M}(T,H)$ of high field can be rescaled into a universal curve, verifying the high-field paramagnetic to forced ferromagnetic transition is of a second order. The well-established scaling behavior of the magnetization and the magnetic entropy change further supports ${\mathrm{EuSn}}_{2}{\mathrm{P}}_{2}$ as an axion insulator.