There were ------- days below freezing last winter.

Use 'fewer' for countable nouns (days, people, items). 'Days' is countable, so 'fewer days' is correct. 'Few' can also work but is less precise here. 'Less' and 'lesser' are used for uncountable nouns (less water, less time) or for comparative degree (lesser importance). This distinction between countable and uncountable nouns is a key grammar rule.