We were there this year at almost that same exact time and it was absolutely awesome! It was our first trip ever as a family and we couldn't have had a better week to do it.
We were there for 7 days and 5 of them were above 70 degrees. The last two were a little rainy but still nice temperature wise so we put on ponchos and had a great time. I guess we had an above average week according to some we talked to.
I can't say enough about how nice it was that time of year though. We did everything we wanted to......never waited in a line longer than maybe 15 minutes and that was Kali River Rapids in AK.....never felt crushed by crowds....saw every parade in a great spot without being there an hour before.....only made one PS reservation from home, walked into every restaurant we wanted to without waits....rented boats one day at Fort Wilderness campground where we stayed and swam another.
Compareatively we went again this June (won the trip, believe it or not) and we will never go at that time of year again! In January we covered every park in a day, going back to our favorites or a few things we missed on our extra days. In June, we were lucky to do about 5 rides in the MK and the heat and crowds were unbearable.
I just kept checking the weather online up till we left in January. I was kind of packed for any weather but like others have said, it is much more pleasant to go and have to wear some layers than to suffer through the heat.
Hope you have a wonderful time!