I have gone in the last week of January for the past five years... ADR's are not that big of a deal for this time. Every year I make 1 ADR for our anniversary (California Grill, Artists Point, V &A's etc), and do the rest as I feel like it.
I have NEVER had a problem getting into Liberty Tree Tavern, L'Originale in Italy, Fantasmic Packages, etc. If you are flexible, you are fine.
Now on the other hand if it is something you absolutly cannot live without then book it in advance.
Jennifer