As opposed to this, if you plan to stay overnight on winter trips (e.g. in the Alps) you don't just want to survive, you want to have a relatively comfortable night. Of course you bring an isolation pad and a sleeping bag with you. Besides that, what equipment do we need and what features do we have to look for?
If you are going to alpine area, your most important concern has to be security. Even with best equipment, knowledge about the dangers and how to avoid them is far more important. As you specifically asked for equipment, I will address these points.
The only way I know of to spend a cold winter night comfortable is in some sort of a snow cave. There are multiple ways to build one, in all cases you need a good shovel. Look for an aluminium one (compound materials tend to brake fast) with a big blade and a D-shaped handle.
If you are in uncontrolled areas you need avalanche rescue material. You need an avalanche transceiver, a probe and a shovel. The shovel can of course be the same one you use for building the snow cave. With modern 3-antenna transceivers by Mammut or Pieps you can do nothing wrong, Arva brought good models to the market lately too. The probe you can also use building the cave for guidance when digging and making holes in the cave walls for air circulation.
Then take a gasoline stove with you. A propane stove works too, but in high altitudes gasoline works better.
As you mentioned bivy bags: I generally don't use them in snow caves, as they keep moisture inside (even breathable ones to an extend). You don't have direct exposure to snowing, so why bothering using one. Far more important is an accurate sleeping bag and well sized isolation pad. The importance of the pad often gets underestimated, get a fat one!