Molecular dynamics simulations are used to investigate heterogeneous ice nucleation in model systems where an electric field acts on water molecules within 10-20 angstrom of a surface. Two different water models (the six-site and TIP4P/Ice models) are considered, and in both cases, it is shown that a surface field can serve as a very effective ice nucleation catalyst in supercooled water. Ice with a ferroelectric cubic structure nucleates near the surface, and dipole disordered cubic ice grows outward from the surface layer. We examine the influences of temperature and two important field parameters, the field strength and distance from the surface over which it acts, on the ice nucleation process. For the six-site model, the highest temperature where we observe field-induced ice nucleation is 280 K, and for TIP4P/Ice 270 K (note that the estimated normal freezing points of the six-site and TIP4P/Ice models are similar to 289 and similar to 270 K, respectively). The minimum electric field strength required to nucleate ice depends a little on how far the field extends from the surface. If it extends 20 A, then a field strength of 1.5 x 10(9) V/m is effective for both models. If the field extent is 10 angstrom, then stronger fields are required (2.5 X 10(9) V/m for TIP4P/Ice and 3.5 X 10(9) V/m for the six-site model). Our results demonstrate that fields of realistic strength, that act only over a narrow surface region, can effectively nucleate ice at temperatures not far below the freezing point. This further supports the possibility that local electric fields can be a significant factor influencing heterogeneous ice nucleation in physical situations. We would expect this to be especially relevant for ice nuclei with very rough surfaces where one would expect local fields of varying strength and direction.