Background: Healthcare workers, particularly nurses and apprentice nurses, are at high risk of the development of hand eczema due to daily exposure to wet work. This study aimed to assess the occurrence of hand eczema in a group of first-, second-, and third-year apprentice nurses at the University Hospitals of Trieste (northeastern Italy) during the COVID-19 pandemic. Methods: Two hundred forty-two Nursing School students were recruited. Data were collected using a standardized questionnaire based on the Nordic Occupational Skin Questionnaire, and all patients underwent a medical examination to evaluate their skin condition based on standard scores. Transepidermal water loss was also measured. The factors associated with hand eczema were investigated using univariate and multivariate logistic regression analyses. Results: The prevalence of hand eczema was low in students both before and after the traineeship (17.9 and 21.5%, respectively), but clinical signs of mild skin damage, mainly skin dryness, were present in 52.3 and 47.2%, respectively. The factor associated with hand eczema was a personal history of atopic eczema (odd ratios 2.61, 95% confidence intervals 1.18–5.80), while exposure to irritants and glove use did not reach statistical significance. Conclusions: Our findings might be explained by the preventive measures adopted for skin protection among healthcare workers in Trieste since the apprenticeship.