Now that we have Freddy's gameplay trailer, we've got a look at his moveset as well. It's hard to tell what would be the enhanced version's effects at this point, but here is what we could see:

**Now updated with official names from movelist, where applicable. [ ] indicates an unofficial name.**

[High Claw Swipe]
Seems to greatly resemble Skarlet's blade uppercut attack where he dashes back and then does a pop-up swipe to set up juggles and what not (or continue juggles, since at least one of his combos also ends in a pop-up). It may not be a special move since it wasn't listed in the special move list.

[Low Claw Swipe]
Same as above, but hits low and knocks your opponent away. Possible wall juggle if they're close to the edge? Also possibly not considered a special move.

Hell Spike (EX: Hell Blast)
Freddy stabs into the ground and giant claws pop out, can do it at close, medium, or far range. The claws also function as a pop-up, hinting that Freddy is going to be a juggle intensive character.
Close: Down, Back, FP
Medium: Down, Foward, FP
Far: Down, Back, Forward, FP

Freddy Fingers (EX: Freddy's Edge)
Freddy sends out at arm that crawls across the floor and hits someone. It's basically a low-hitting projectile.
Command: Down, Back, BP

Glove Toss (EX: Power Glove Toss)
Freddy seems to throw his hands (or a pair of hands at least) at you. Hard to tell much else beyond the fact that it's a projectile. Looks kind of slow compared to other projectiles though.
Command: Back, Forward, BP

Sweet Dreams (EX: Deep Sleep)
Freddy makes a gesture and a green blob falls (kind of slowly) from the sky directly above your opponent. If it hits them, they seem to be dazed. So it's basically a free hit move if it connects much like Sub-Zero's freeze, Cyrax's net, or Kabal's dash. Considering how slow it looks, it will probably be hard to hit with it unless you catch your opponent in the middle of something else like he did in the video. It only lasts for about a second.
Command: Down, Forward, BK

Dream Shift (EX: Hell Shift)
Seems to be your standard teleport but he has two different versions (away and towards) and they seem to go a set distance so you may or may not end up in front of your opponent.
Forward: Down, Forward, FK
Away: Down, Back, FK

Throw
Freddy grabs his opponent, shushes them, then stabs and tosses them away.

X-Ray
Freddy lunges at his opponent from about jump distance away for a double claw to the chest and then claw to the face. The opponent is knocked away at the end so it cannot be combo'd afterwards.

Fatality 1: Tell 'Em Freddy Sent Ya
Freddy drags his opponent into a fiery pit and it squirts up blood.
Command: Back, Forward, Down, Down, FP (Jump Distance)

Fatality 2: Name Unknown
Freddy summons a furnace and hurls his opponent into it, burning them alive. When they try to escape he slams the door, chopping off their arm in the process.
Command: ???

From what we can tell, he seems pretty fast and has a wide array of tools to make him a contender. Considering his variety of pop-ups, he'll probably rely a bit on his juggles.

What do you think?

*thanks to drpvfx for some corrections!*