The following from Mousesavers.com:
"If your stay STARTS in a particular season, but runs into the next season, your room rate will be based on the season in effect when you check in. For instance, if you check in to your hotel for a one week stay on February 14 (Value Season), even though Peak
Season starts on February 15 you will be charged for the entire stay at the Value Season rates."
"Keep in mind that this can work against you if, for instance, you check in during Peak Season and the rate drops to Regular Season during your stay. If you want to avoid paying the higher rate for your entire stay, you can make two reservations and split your stay when the season changes. You will have to check in and check out on paper, settle up any charges to your room and get new keys. There is a remote possibility you may have to change rooms. But this may be worth it if you save $50 a night! If you do this, it's a good idea to call the front desk at the resort five days prior to arrival and point out that you have a continuing reservation and would like to stay in the same room. This usually works. Be aware that when the season changes, there can be a long line at check-in with guests taking advantage of the lower rate. Either do the check-out/check-back-in process early, before you go to the parks, or call the front desk and ask if you can do it later."