We went the first week in February 2 years ago and the only thing that was closed was Splash Mountain (which is normal over the winter) and both of the waterparks were closed (again normal over the winter).
We didn't miss them because it was our first family trip (1st trip for me, oldest son, and youngest daughter --- my hubby had been 25 years before when he was in college --- our oldest daughter and youngest son had been 2 years before with their grandmother)
There were SO many things to do! That first trip was overwhelming! I figured I was prepared for Disney because we'd had season passes to Busch Gardens for years.
Uhhh..no comparison! I spent much of that first trip with my nose buried in a guide book or a park map.
If this is your first trip to Disney...you won't miss the one or two rides that may be closed...and most of those are water rides that you likely wouldn't want to ride in February. (During our trip only one day was it warm enough to go swimming -- I think it hit 75 that day...the rest of the trip, it was mostly in the 60s.)
And yes...I would avoid early March! We went the 1st week of March last year and it was college spring break week -- weather was warm but WOW it was crowded!
It also depends on when Easter falls...if Easter is in early April...probably the second or third week in March wouldn't be too bad. The worst weeks for Spring Break crowds is the 1st week of March and the 2 weeks before and after Easter.
For instance -- I know in 2014, college spring break week for most schools is March 1st through 9th. So avoid that week. Easter isn't until April 20th. So avoid all of April. As for March travel, you'd be fine with any dates in March from the 10th onward. March 15th through 22nd would be good and so would March 22nd through 29th.