We went to DP 2years ago in March children 4 and 2.5, it was verry cold ( there was a cold spell here as well). We had a great time.
New York New York ,rooms good,was closest to park other than Disneyland Hotel ( over entrance of park) i think there was a fridge, but I am sure if you contacted hotel they would put one in room as a special reqest for medical reasons, wherever you decided to stay at ( well I would like to think they would).
Healthy Food difficult to find, but one thing we did which helped was order breakfast to our rooms, it mean't we had a totally relxing breakfast and we ordered fresh fruit, which we could let children snack on as and when. Thye always served lots of fruit, ham, fresh rolls - so we made up a little packed lunch (sshhh) .
We did try to get healty food and went to the rainfirest cafe, this was just ok, nice place, food not that great, more of the same really, fisn h chips, sausages ad chips.
The golden arches (MCD's) was the best at least you could get carrot batons etc.
I would not worry too much about it being busy, Disney know what they are doing as far as dealing with crowds and there is always so much going on - parades, shows.