Background: during the COVID-19 pandemic, psychological burden increased. Contact restrictions were predominantly stressful for families. Parenthood was reported to be especially challenging for parents of preterm children. Material and Methods: a cross-sectional online-based survey on the psychological burden of parents of preterm and full-term born infants and toddlers during the second lockdown of the COVID-19 pandemic in Germany was offered by social media, webpages, etc. Generalized Anxiety Disorder-7 (GAD-7), Patient Health Questionnaire-2 (PHQ-2), COVID-19 Anxiety (C-19-A), COVID-19-related child protection behavior (PB) were used. Results: 2742 parents—predominantly females—took part in the study, 2025 parents of full-term and 717 parents of preterm born children. Female caregivers of full-term children reported significantly more depression symptoms than those of preterm children during the second lockdown of the COVID-19 pandemic. The PB correlated with increased COVID-19 anxiety as well as with increased generalized anxiety and depression symptoms. Female caregivers of preterm children showed significantly more protection behavior than those of full-term born children.