If you are exempt from the FLSA, which means that you are salaried and not eligible for overtime, and the office closes because of heavy snow and/or state emergency your employer is required to pay you your normal salary, as long as you have worked in that workweek.
Your employer may require the use of vacation time, paid time off or other accrued paid leave, but if there isn't any accrued paid leave, your employer still has to pay you.
Your employer isn't required to pay if he/she is open for business and you have difficulty to come in - because the road is unsafe, or your children are still at home for a snow day. In that situation, if you don't have accrued paid leave he/she may take a deduction from your salary for the work missed. Another option is asking your employer, if possible, to work from home so no pay would be missed.
If you are a nonexempt worker, which means eligible for overtime, and the office closes, your employer is not required to pay you according to the law. However if your employer closes the company during a working day, he/she does have to pay you for the hours you have worked. In some states employers have to pay their employees a minimum number of hours if they have reported for work. Please check the state laws on this.