Maize is the most widespread and, along with wheat, the most important staple crop in the Republic of Serbia, which is of great significance for ensuring national food security. With the increasing demand for food and forage, intensive agricultural practices have been adopted in the maize production systems. In this direction, considerable research efforts have been made to examine the effects of different types of cover crops as a green manure on maize productivity; however, no consistent conclusions have been reached so far. Therefore, the objective of the present study is to examine the possibility of predicting the effects of winter cover crops (CC) integrated with different management practices on the morphological traits, yield, and yield components of maize. The experiment was carried out on chernozem soil from 2016 to 2020 as a randomized complete block design arranged as a split-split-plot with three replicates. The pea as a sole crop (P) and the mixture of pea and triticale (PT) are sown as winter CC with the following subplots: (i) CC used as green manure, and (ii) CC used as forage and removed before maize sowing. The artificial neural network is used for exploring nonlinear functions of the tested parameters and 13 categorical input variables for modeling according to the following factors: CC, way of using CC, N fertilization, and year. The computed maximums of plant height, number of leaves, number of internodes, plant density, number of ears, grain yield, 1000-grain weight, hectolitre weight, dry matter harvest residue, harvest index, leaves percentage, stems percentage, and ears percentage are as follows: 232.3 cm; 9.7; 10.2; 54,340 plants ha−1; 0.9; 9.8 t ha−1; 272.4 g; 67.0 kg HL−1; 9.2 t ha−1; 0.52; 18.9%; 36.0%, and 45.1%, respectively. The optimal result is obtained with peas used as green manure, with 50 kg N ha−1 and in the climatic conditions of 2018. Consequently, maize production under subsequent sowing periods can be successfully optimized by adapting selected management options for higher yield accomplishment.