For those who received any kind of formal instruction, it wasn't a daily affair. Learning typically involved apprenticeships, oral traditions passed down within families and communities (poetry, storytelling, history, skills), and religious instruction from druids (if applicable). The frequency and intensity of this learning varied considerably. Sons of chieftains or those from privileged backgrounds might have received more structured instruction, but even then, it wouldn't necessarily be every day.
Therefore, the answer is a definitive no. Celtic children did not have to go to school every day because there were no schools as we know them.