HH can be nice year-round. December-February may have questionable weather, but the area still has a lot to offer. March-May will have weather ranging from 60's- 80's, but the ocean will still be cool (pools are heated though).
June thru August is the busiest time of the year at HH and everything is in full swing. Ocean temps will be in the mid 80's thru September before cooling off.
Crowds drop after Labor Day but the activities are great thru October due to the great weather and pleasant ocean temps.
Besides summer months, the island draws big family crowds during spring break months (late Feb- April) and around Thanksgiving.
The Disney HH resort itself usually has good availability at 7 months for 2BR villas for all times and for 1BR and Studios much of the year. Summer,Spring Break and Thanksgiving dates are more competitive at 7 months. There are only 21 Studios and 1BR villas and 5 GV's at the resort.
Enjoy!