I have seen several websites that list it as wheelchair accessible, but i think they are confusing it with King Arthur's Carousel at
Disneyland or Carousel of Progress; both of those are accessible, but the MK carousel is not.
It is listed by Disney as "must transfer", but I think it should really be listed as "must be ambulatory".
I had some pictures, but can't find them, so I found a video instead, that shows a bit.
There is a particular gate to go in, marked with a wheelchair symbol. But, once you enter the gate, there is a step up to the carousel platform. As lanejudy mentioned, there are some chariots with as well as horses, but you have to get to the chariot, which is toward the middle.
The handicapped entrance gate is shown in this video at about point 1 minute 20 seconds and 2 minutes 11 seconds. You can see the edge of the platform - kind of a pink line going around.
http://allears.net/tp/mk/carr.htm