My DD is 3 and we are doing WDW as well as a 3 day Disney cruise next month, so I guess we'll find out how it goes. I think the big thing is to have realistic expectations. If your kids are nappers, they will still need to take a nap - if you try to go, go, go, they will end up overtired, hungry, and then are more prone to have a meltdown. If you do any of the Disney parks, make it a point to have some downtime in the middle of the day - even if they are not taking naps, at least everyone can relax. Kids at that age can also freak out and not want to see or take pics with the characters because they are scared. Don't force them. There will be ride and attractions that your kids will be too small to go on but you can get Fast Pass for the rest to try to keep the line waiting to a minimum.
We went to WDW 10 years ago when my stepsons were 6 and 7 and rented a condo for the week. It was the best thing we could have done - much cheaper, saved money on eating, more space to spread out. We are doing the same thing this time around (except for when we are on the cruise, of course). We were less than a 10 minute drive from the parks. The Nickelodeon Resort is NOT part of Disney.
We are going to be on the new ship, the Disney Dream, and it looks like it should be awesome for our 3 year old - she loves to swim so just a pool alone should keep her happy but they also have special play rooms with Toy Story and Finding Nemo themes. There are chat forums on-line that are just about Disney and you can probably find a lot of good feedback from other people on there about the parks, the cruise, etc.
Average high temps in Feb are around 74, looks like March and April it's around 78. If you try to go at a time when there are no school vacations, hopefully it will be a little less insane.
Finally, when DH and I were discussing doing a Disney trip with our daughter at 3 years old, I brought up the same thing that a lot of people will say - she probably won't remember it (though she does seem to remember a lot of things really well and there will be plenty of pictures). DH's reply? "But we will!". Plus, it's not like we can't go back again in 4 or 5 years.