Background: The SARS-CoV-2 Omicron spread fast globally and became the predominant variant in many countries. Resumption of public regular life activities, including in-person schooling, presented parents with new sources of worry. Thus, it is important to study parental worry about the Omicron variant, willingness to vaccinate their children, and knowledge about school-based COVID-19 precautionary measures. Methods: A national, cross-sectional, pilot-validated online questionnaire targeting parents in the Kingdom of Saudi Arabia (KSA) was distributed between 31 December 2021, and 7 January 2022. The survey included sociodemographic, COVID-19 infection data, parental and children vaccination status, attitudes towards booster vaccine, parents’ Omicron-related perceptions and worries, and attitude towards in-person schooling. Results: A total of 1340 participants completed the survey, most (65.3%) of whom were mothers. Of the parents, 96.3% either received two or three doses of the COVID-19 vaccine. Only 32.1% of the parents were willing to vaccinate their young children (5–11 years of age). In relation to their children 12–18 years of age, 48% had already had them vaccinated, 31% were planning to vaccinate them, and 42.8% were willing to administer a booster dose. Only 16% were more worried about the Omicron variant compared to the Delta variant. Residents of western KSA were more worried about Omicron compared to Delta. Parents worried about the Omicron variant and male participants were significantly less aware of school-based COVID-19 precautionary measures. Parents with post-graduate degrees and those having more children were significantly more inclined to send their children to school even if COVID-19 outbreaks could occur in schools, while parents who were more worried about the Omicron variant and were more committed to infection prevention measures were significantly less inclined to do so. Conclusions: Overall, parents had lower worry levels about the Omicron variant compared to the Delta variant. They had a higher willingness to vaccinate their older children compared to the younger ones. In addition, our cohort of parents showed high willingness to send their children to schools and trusted the school-based preventative measures. These findings can inform policy makers when considering school related decisions during the current or future public health crises.