The growth of a two dimensional square ice formed from arrays of nanoscale magnetic islands was simulated. Ordering of the magnetic moments was investigated as a function of growth rate, island aspect ratio, and island pitch. Arrays of islands with low switching fields and slow growth rates showed the highest degree of ordering in the as-deposited state. Subsequently, simulations of annealing were carried out in which islands were heated to the Curie temperature and cooled at various rates. Slower cooling rates left the island arrays in states with higher order. The level of ordering that could be achieved in an array of islands was found to be closely linked to the ratio of the average magnetostatic field acting on an island to its anisotropy field.