I would not mow it at all unless it gets up to 5 inches. What you need to develop in the winter is deep roots so the grass can withstand the summer heat. Grass kept short will develop short roots. Tall grass has more chlorophyll to make more sugar and can develop deeper roots. Set your mower to the highest setting and wait until the grass is tall enough to mow.

As for your fertilizer, I'm a little offbeat with most here. I think applying fertilizer along with the seed is a waste of money. Fertilizer does not work unless you have roots to suck it up. Seeds have no roots. In fact I don't think your roots do much of anything except absorb water until the grass gets tall enough to mow (5 inches). I always suggest you wait to apply fertilizer until the second time you mow (at 5 inches, not to beat this horse any more). By then you have some deep roots and your fertilizer will be absorbed as it moves deeper and deeper in to the soil.

Getting back to the specifics of your question, it sound like you are mowing too low. Assuming it has been mowed once already, I would let it get taaaaall enough to mow once more and fertilize.