We did a sleigh ride at the Fort in December 2021 - (this was before online bookings were available for this specific offering), but we did manage it (we booked by phone as soon as it opened and there was only one slot available). However, when we actually went there during our stay, there were plenty of walkups available - there was a CM there and people could just put their names down for same-day rides.
Don't know if it is the same nowadays (it's only been two years!) but it may be worth a shot to just walk up and ask when you are there!