How long should a boat's interior dry before winter cover-up?

A full day with hatches and doors open is a reasonable minimum -- an hour with a fan running is not enough to prevent trapped moisture in cushions and carpet.

Does a mildew inhibitor spray replace proper drying?

No. A mildew inhibitor is a second layer of protection on top of full drying and airflow, not a substitute for either -- spraying it on damp upholstery still leaves the moisture that causes mildew in the first place.

Where does musty smell in a stored boat usually come from?

A damp bilge is one of the most common sources, even when the cabin and upholstery look and smell fine at cover-up time -- check it specifically before closing up for the season.

Winterizing a Boat's Interior: Mold and Mildew Prevention During Storage

How to prep a boat's interior for months of storage without trapping the moisture that causes spring mold and mildew complaints.