We were there the week following NYE 2 years in a row for the marathon and it was cold! Especially in the morning. I'm talking coats, gloves, hats. The first year we weren't prepared for it. We wore long sleeves all day, but ditched the jackets in the afternoon. I'm sure it varies year to year, but if I were to go back again that time I'd be prepared with sweaters and scarves. The one day it rained all morning and the high was in the 50s (if it even hit that). We were on the Keys to the Kingdom tour so we were outside a lot and I was frozen.
There were carts selling hats and gloves in the parks. They were expensive though.