You can restock sugar bricks in pretty cold temps. I'm in northern NY and I had to do it in the mid/high-20s once or twice this winter. Because the bricks are stiff (unlike pouring in a bag of sugar, etc., Mountain Camp style), all you need to do is choose a NON-windy, sunny day, have the bricks close at hand (I usually have both whole bricks and some chunks to choose from as you can't waste time fiddling around to get the right fit and placement at those temps.), and just tip the front of the box up, locate the open space and pop a piece in. You can do it in just seconds, and generally the bees stay quiet and let you do it. Sometimes I even had to gently push aside hanging festoons of bees to make room for the refills.
I prefer to do it in temperatures when any escaping bees might have chance to survive for the few minutes to re-enter the hive through their entrance, but if the choice is that they all starve, I'll let a few take the hit. The biggest difficulty I had with it was removing the outer layers of insulation to make it possible to tip the quilt box up. Next year my insulation plans will keep that in mind. (I removed the heavy wood tele cover before doing the tipping, relying on the shavings in the QB to keep everyone warm for a few minutes. If you aren't using a QB, then I'd leave the inner and outer cover on and just tip them up and plop in the bricks on the bars.)
I used the sugar brick recipe here on BS from Lauri. I must say my bees were flat out nuts for those bricks.
I found that having a fabric floor on the QB not only kept all the mess from the shavings out of the hive but also apparently made a cozy surface for the bees to cluster on during the day. When I opened the boxes to check or restock the bricks I had tons of bees hanging from the fabric. The space inside the feeding rim was always quite warm and I think the bees liked that. The fabric worked very well at allowing any moisture to pass through and on in to the shavings (and eventually out of the hive). Since I am a new beekeeper, and was using the QBs for the first time, I often opened the tele cover and and burrowed down through the shavings with my bare hands to check on whether they were getting too wet (never happened). It was also fun to touch the top surface of the fabric and "tickle" the feet of the festooning bees below. I only did this AFTER I'd finished up restocking. The bottom layers of the shavings were often in the high 80F. Very cozy! I suspect that in the cold your bees may have tried to get into the shavings, perhaps creating an avalanche, as you described it. One issue about using a pillow case is that it may allow the shavings to be narrower (less thick) at the box margins creating cold spots because pillow cases are flat-constructed, not box-constructed. A fabric floor is easy to install; the hardest part is the need to get it to be very taut because the weight of the shavings will cause it to belly down a bit. I lost some bees because of this when I was using thicker than usual bricks and they got squashed on the top of the bricks. I plan to increase the height of the feeding rims by 3/4 of an inch or so next year to avoid this issue..
Enj.