Maybe, maybe not. Thus far this winter in my zone 5 garden
I have seen only one night when temperatures dropped near zero otherwise it has been slightly above average, Moisture plays almost as much a part of the digestion process as does Nitrogen, if there is too much moisture the wee critters that digest the material cannot get the oxygen they need to work no matter how much N is present.

If your temperatures are getting well below zero every night it may well be too cold for the bacteria to function.

kimmq is kimmsr

I tend to agree with Kimmsr. You might want to wait until winter begins to wane a bit and then add some urea and turn the pile and then add some more and turn again. My piles here is Missouri 6a are usually frozen on top in the winter but this year has been pretty mild so far with no lows below 20 and daytime highs above freezing. That will end this weekend when we are supposed to get single digit lows for a day or 2. I don't think my piles are hot right now but they appear to still be shrinking slowly.

I will wait until late February or early March and then merge my 5 fall started piles together into 2 or 3 while adding urea at the same time. When the grass starts to grow I will start building some new piles using 20 or so bags of chopped leaves I saved from fall, fresh grass clippings, and a few 5 gallon buckets of chicken manure that I accumulate over the winter.

I do most of my intentional, active composting over winter because there is not much else to do in the garden. I add urea to transfer station material, leaves, and brush that I chip myself. It was below 20 one recent morning, and my piles were still hot.

If it gets cool and still smells like wood or leaves, then I will add more urea. If it smells earthy, I leave it be. If its too chunky, i might screen it. but usually it is fine as-is.

I've found clear plastic sheeting over a pile in full sun keeps it hot, regardless of what mother nature throws at me.

Clear plastic sheeting----now that's an idea. The tarp seemed to attract mice.

I'll continue to slowly trickle urea on there. The chunkiness of the wood chips seems to at least be immune to the soggy aerobic mess. It does get above freezing most days, so it's not like an ice cube most of the time.

'I'm in a reasonably cold zone---5. It gets well below zero every night'

Did you mean to say that it gets well below freezing every night or well below zero? Big difference in the 2 and if you can maintain a hot pile during the winter.

Well below freezing--sorry.

If your composting method gives you finished compost in the spring when you need it, I wouldn't think there is any compelling reason to add nitrogen in winter. That costs money and there's a fairly good chance it will just leach out unused.

Of course the 'trickling' method can be done with free urea, if you know what I mean. :-]