Whether you get charged or not is inconsistent.
As ducklite mentioned, it used to be free of charge for medications, but as more people found out about it, more people were asking (most who actually didn't have any medication). So, WDW started charging everyone. People even posted that they were told if they didn't want to be charged, they could keep their medication behind the front desk - even if that meant several trips a day to get doses!

This was even when some people dealt with WDW Resort Special Reservations (the department that arranges special assistance):
(407) 939-7807
(407) 939-7670 [TTY]
In the past year, more people have been posting that they were not charged. So, I would suggest making sure your medication is in a bottle clearly marked that it needs refrigeration. You could try calling Special Reservations, since some people have noted recently that's how they arranged a frig at no charge.
Mention your need to the front desk when checking in (and ask to speak to the manager, if the front desk person says no). Check your statement for a charge when you check out and if you find one, ask to have the charge waived.