You'd have to assume any food given your lawn's turf at this time is going to encourage new development of grass.
If you were to go by your local average frost date, you might be better to hold off giving any more fertilizer and make a point of feeding your lawn next spring.
What you've done is probably going to assist the lawn to make a good showing next spring so take that into consideration when and how much you put down at that time.

Soil test...soil test...soil test!!!!! If you didn't do this before you planted, you need to do this now before you apply any more nutrients. You cannot possibly know what nutrients are needed without a soil test.

Yesterday would have been an ideal day to put down fertilizer. The temperatures are in the mid 60's today with lots of rain.

It is getting late, but I still think you can do an application this weekend. I did a quick check of the weather for northern Virginia. I saw daily highs in the mid 40s.

Your goal is to apply 0.75 to 1.0 pounds of nitrogen per thousand square feet. You don't need any phosphourous and very little if any potassium. The bag does not have to say "winterizer" or "winterguard". Any fertilizer (no weed and feed) will do.

The roots of the new grass plants will continue to grow even after the top growth has stopped. There is no harm in applying fertilizer even if the temperatures drop dramatically. In the worst case scenario the grass goes completely dormant and the nitrogen washes out of the soil before the plants have a chance to use it.

Mike, as with some others, people try to associate the weather to how their gardens grow, including how the grass grows.
All our plants grow in soil....not in the air. While the ambient weather in any local environment has a bearing on how our plants grow, its because the weather improves over long periods which can then, affect soil temperature.

Because you have a warm spell in January...let's call it, the January thaw...when temperatures might go up and up...and make us believe spring is around the corner.
Unfortunately, the deep freeze returns and we are reminded that Ma Nature can be cruel to us gardeners.
You wouldn't think to go out and plant spring plants during this spell...then it follows we shouldn't plant when a warm day arrives in the fall when its just as likely to fall into the deep freeze...snow is always around the corner.
Plants don't grow in a day...so a nice 70's 80's even, does not suggest that the next day might be in the 40's or lower. Down the road is how we must assume how temperatures behave and for that reason, we do let our plants go into dormancy...and while our lawns are not usually thought to go into dormancy, they nevertheless go to sleep until awakened in the spring with multiple days of warmth to encourage the soil temperature goes up and makes grass seed, grass growing, viable.

Dont' think today....nor tomorrow, think next week, next month...and you wont confuse soil temperature with air temperature.

I agree, the root growth is dictated by soil temperature. If the temperature was scheduled to drop into the low 20s this week, then I would think the window of applying fertilizer has passed. The nitrogen can't enter the soil if its frozen.