There are mosquitoes at WDW. I've seen them when we've been there in August. We stayed at ASSports in August 1997 and came back to the resort from the parks one evening to find a message from Disney on our bed. It stated that due to an outbreak of St. Louis Encephalitis (It is one of several mosquito-borne virus diseases that can affect the central nervous system and cause severe complications and death.) they were suggesting that all guests use bug repellant (available in the resort gift shop) and if we went out in the evening to completely cover all exposed skin. I had 5 bites just walking from the bus to our room before reading the note. The next morning there were mask-wearing men walking around the resort using portable sprayers to spray the gardens and grass right up to the doors of the rooms. I was glad we were leaving for home that day, I didn't like the idea of breathing in what they were spraying around.
That said, I have been to WDW twice in February and have never seen mosquitoes at that time.