With your 35 degree temp marginally above freezing, as long as the egg hasn't cracked it will be fine. Just put in fridge to "warm" up slightly and use fairly soon.
We run our fridge at 4 degrees C, so that's a bit over 39F so what you are looking for is to raise the temp more slowly than room temperature will give.

We don't have snow here, but do get some frosts. I only ever keep my eggs at room temperature, but it is the coolest room. South side of house in laundry. Oh and so as not to confuse you, we are Southern hemisphere.