Are you staying on a cash reservation booked through Disney? If so, you should get clean towels every day, along with full cleaning just as in a Disney hotel.
Or are you staying on DVC points (your own, or rented)? If so, you'll get clean towels on day 4 (and days 8, 12, etc. if you stay that long) as part of Trash & Towel Service and Full Cleaning (schedule depends on how long you stay - if 7 nights or fewer, T&T on day 4; if 8 nights or more, Full Cleaning on day 4 and T&T on day 8 then alternating every 4 days). (FYI day 1 is the day you check in.) If you need clean towels in between, you can wash & dry them yourself.