You're going to need spending money. Probably more than you imagine. The Walt Disney World resort in Florida accepts the currency: US Dollar. The hotels and parks accept cash and cards just like places do over here.
The Exchange Rate
The exchange rate from the British Pound to the US Dollar does fluctuate. At the time of writing in early 2017, the Pound is quite weak, so going abroad is more expensive.
For a quick look at the current exchange rate, you can see our exchange rate widget on the right hand side of the page. You will expect to pay (either at currency exchanges or charges on your card) around 0.5 less than the real exchange rate. For example, if the exchange rate is 1.35, expect to get around 1.30.
The preference of cash comes down to your own opinion. Cash is much more convenient, but if you lose cash, it's gone. Plus you'll have to deal with change, and working out foreign currency coins in a country you've not been to all that often, can be frustrating.
Credit Or Debit Card
Using your normal bank debit card is not recommended. The charges are usually high, and it just adds to an already expensive holiday. Getting a 0% credit card for purchases abroad is a much better solution, as long as you don't go too crazy! Either way, tell your bank that you're going abroad, just incase their security system kicks in and blocks your card.
Travel Money Card
Some travel agents try and sell you their travel money card. These are usually OK, and work like most credit cards. You can load the money on whenever you like, then spend it abroad as normal. They are usually free to use, but tend to charge you withdrawing from ATM's.
You should take at least some cash. You'll need cash for things like tips, (such as hotel house keeping), although restaurant tips can be paid using your card, too. It's also good to have some cash just incase you get problems with using your card abroad.
There are ATM's thoroughout the hotels and parks, if you do need to withdraw any cash.