A systematic and meta-analytic study (analysis of 23 studies) examining the effect of cow's milk on iron deficiency in infants up to 3 years of age found that cow's milk consumption was associated with an increased risk of developing iron deficiency.
As stated, "Limiting the consumption of cow's milk can be important to ensure adequate iron intake for infants and toddlers."

The mechanisms that seem to be responsible for this deficiency may include low iron content of cow's milk, blood loss from the intestine that occurs in 40% of newborns who consume cow's milk (mainly for the first year of life), as well as its very high content of Calcium and casein (protein present in 4-fold amount compared to human breast milk), substances that act as inhibitors in the absorption of non heme Iron.
Also as mentioned, the high concentration of casein and electrolytes in cow's milk can affect the kidney function of the newborn (due to high concentration of urea) and lead to severe dehydration due to renal failure in balancing body fluids.

Post-analytical research on Iron deficiency in infants and newborns:
https://www.ncbi.nlm.nih.gov/pubmed/25989719

Mechanisms that may be involved in Iron deficiency.
https://www.karger.com/Article/Pdf/106369