If the tree is not frozen, there is slow metabolism. If temperatures are below +4 C, or 40 F, metabolism is slow enough that for practical purposes it can be viewed as zero. If the soil is above 4 C, and the top is chilled enough to stay dormant, roots indeed will grow over winter. If the tree was starving for fertilizer going into autumn, it might be good to use a LOW DOSE, but a healthy tree stores a fair amount of nutrients for use later. So there normally is NO NEED, to fertilize in winter. If you feel you have enough happening in winter to warrant fertilizing, use a dilute solution, perhaps around a quarter or one eighth. of the normal label dose rate.
Separate point. It is a myth that low or no nitrogen fertilizers are required in autumn. Came out of research 9n the late 19th century that neglected to identify that at the trials a heavy dose of nitrogen was being delivered to the plants by acid rain. Heavy pollution from coal heated homes around Kew gardens in the 1870's & 1880's meant that rain in autumn, after the heating season began, the rain washed nitrates and sulfates out of the air onto the test plots the researchers at Kew were using. At that time they did not identify this as a significant source of nutrients. Kew published, and every gardening book for hobby growers published afterwards, repeated these results over and over until it became ''received wisdom''. Nutrition research is expensive, and tricky. Most authors will simply cite old research rather than try to do some new research. Michigan State University did a very comprehensive study of plant nutrition for plants in horticultural production settings beginning in about 1980 thru 2010. One result is the public domain formulations for fertilizers referred to as MSU formulas. Hit their website for more information.
High phosphorous is not only a waste of money, and not what the plant needs, excess phosphorous can itself cause symptoms of nutrient imbalance. Consult a text for details but clearing of pigment from parts of leaves (pattern opposite to calcium deficiency) can result. Poor root growth, poor growth in spring can be the result of excess P in autumn.
Turns out 365 days a year the metabolism of plants needs roughly the same ratios of nutrients. A balanced diet of about 13-1.8-4 with 12 calcium 3 Magnesium and the long list of macros and micros. At no time would the plant benefit from high phosphorous. ratios. A ratio of all the same numbers, for example 10-10-10 is NOT BALANCED to the needs of the plant. Think about it, if you consumed as much vitamin D as vitamin C you would die. Similar with plants. 10-10-10 is not balanced. This is from MSU research, the exact ration varies a little, but the numbers I cite are within a percent or two of the average of their many studies.
Okay - so you been not doing what I suggest and your plants are still alive? - Or "Hey Leo, this is bullshit because my plants are not dead, in fact they look pretty good." Answer: Thankfully a flush with clear water leaches out a lot of the excesses and helps the plant correct for the fact that its owner has no clue what it really needs. Water with fertilizer solution, then for the next normally scheduled watering useing clear water with no additives really does help the plant self regulate nutrient levels in its tissues. A lot of excess nutrients end up on the ground, in the runoff, or in the sewer system. A waste but your trees can still look good.
There are few products out in the market that come anywhere near the ideal nutrient demand of plants, so even I use what I can and flush with clear water in between, but I am shooting for eventually having the perfect fertilizer, one that would be equally good in a closed indoor hydroponic set up, and equally good on the trees outside in my garden.