Magnetic reconnection in strongly magnetized regions around the temperature minimum region of the low solar atmosphere is studied by employing MHD-based simulations of a partially ionized plasma within a reactive 2.5D multi-fluid model. It is shown that in the absence of magnetic nulls in a low beta plasma, the ionized and neutral fluid flows are well-coupled throughout the reconnection region. However, non-equilibrium ionization-recombination dynamics play a critical role in determining the structure of the reconnection region, leading to much lower temperature increases and a faster magnetic reconnection rate as compared to simulations that assume plasma to be in ionization-recombination equilibrium. The rate of ionization of the neutral component of the plasma is always faster than recombination within the current sheet region even when the initial plasma beta is as high as beta(0) = 1.46. When the reconnecting magnetic field is in excess of a kilogauss and the plasma beta is lower than 0.0145, the initially weakly ionized plasmas can become fully ionized within the reconnection region and the current sheet can be strongly heated to above 2.5 x 10(4) K, even as most of the collisionally dissipated magnetic energy is radiated away. The Hall effect increases the reconnection rate slightly, but in the absence of magnetic nulls it does not result in significant asymmetries or change the characteristics of the reconnection current sheet down to meter scales.