Embedding vs One Hot Encoding for Multi-class Variables

I was looking at the ‘PromoInterval’ category for the Rossman dataset and it appears to have only 4 categories including NA: ['Feb,May,Aug,Nov', 'Jan,Apr,Jul,Oct', 'Mar,Jun,Sept,Dec']

Suppose there were 10,000 combinations of months (there can be 2^12) - would it make sense to treat each combination as a separate category or at this point would it be better to make each month its own column with a boolean field for each observation.