We do not pay for Holidays during an employee's 90-day introductory period when they first start. Our handbook does not differentiate between exempt and non-exempt in this regard. Do we have to pay a new salaried employ for holidays during this period?

Yes, you must pay exempt employees for holidays. There are only a very few instances in which an exempt employee can have their salary docked, and a holiday when the business is closed, is NOT one of them. Doesn't matter if his first day of work was the day before the holiday; he still has to be paid.

You are, however, free to have a policy where non-exempt employees do not get paid for holidays.