As I've expressed at probably 2 locations in my own site, my general feelings are to avoid fertilizing trees.
Usually, I boost my own little trees to get them away from the dogs and kids, then back off quick.
In our area, the majority of winter damage from wind, and rain and snow on trees, is on the ones belonging to fertilizing programs offered by "chem" services.
The leaves are bigger, and the branches are longer (leverage).
Also, the natural form becomes distorted.
Usually the best trees overall, are the ones that are unfertilized, but in undamaged soil.
One small reason for fertilizing, and it wouldn't exactly be for the tree alone - but if there is organic matter around the tree like bark that it not decomposed, then addition of nitrogen can be helpful for the microorganisms that are taking a toll on the nitrogen supply in the area.
Plant have to have nitrogen. Its one of either 12 (or 13) absolutes that are bare neccessities for plant life.
So when something like bark, or partially decayed compost is applied onto, or into the soil, that can be a reason for applying a strict nitrogen or NPK fertilizer.
Addition of nitrogen would