Never been on the 31st BUT have to many sold out nights. I agree the second parade is better viewing, however, it is not much better than the first as far as crowds go. IF you have a wheelchair, go to the viewing area in Liberty Square for wheelchairs, it is right at the bend, so the headless horseman starts to slow down about the corner and then the horse walks over the bridge down the way.
I would suggest a slow day, lots of resting and a good meal before you go. Enter at 4 or shortly after so you can ride some rides if you want. The dance parties are so fun! We have watched the fireworks for the last several years from behind the castle in the new fantasy land area, good area but more importantly not as crowded.
Have fun!