We get down to a few degrees above freezing on occasions in Adelaide, South Australia and our out side birds are always okay. It can hit 0 but it's rare and always at the coldest part of the night/early morning in winter so it's never really "freezing". This is about the limit of a budgies reasonable tolerance. Other parts of Australia where they are found can get a little colder but they aren't going to do well at 0 for extended periods.
The key is breeze or wind. Budgies are tough, they live in the desert. They don't like to freeze but can keep them self warm when needed by fluffing up an insulating themselves. A breeze and especially wind can cause problems because it blows the heat out from their feathers and away from their body in general, essentially ruining there ability to insulate. If they are shivering, like any animal, it's not good.
Protection from wind can be the difference between tolerant and unhappy and dead. The key ESPECIALLY WITH OUT DOOR BIRDS is this. They need good, well though out shelter.
Think about this...
In the wild a budgie will keep moving until it finds a place that supports enough protection from the wind to survive. Within an artificial environment (which every environment we provide is, no matter how big or small the cage) budgies are limited in places it can move to perch where the wind is minimal (and they still feel instinctually safe from predators). If you ask yourself, "would a wild bird naturally choose to perch and sleep with this much wind" especially when it gets cold, it will tell you if your budgie will be happy through the night.
An indoor cage is easy, wrap it completely in a blanket or cage cover you would consider warm and it's unlikely you will get a breeze that will bother them.
Out door birds need good protection, not a nesting box per se but a well protected area. In a big out door cage you can make it out if wood within the metal cage itself especially the perch (as metal radiates cold, wood doesn't)
If the cage is outdoors and on the smaller side, the type with bars all around in all directions, wrap it when it's cold or cooler and windy if it's exposed. These types of cages offer no wind protection except possibly a limited amount down low where the walls are plastic and a budgie won't sleep low.
If the cage is to big to bring in side make sure it's in an area shelters from wind or create an area (wood surrounds are best) in the cage to do this.
A good high perch in a place well protected from wind gives them the opportunity to move there if they choose if they get too cold on a windy night.
I have seen them sleep exposed on the side of a wire case, side by side (but not close enough to share heat) on very cold nights. They won't always shelter themselves when you think they should, but for our birds, they can when they need to and we have never had a death we suspected was from being cold.
However like all animals they prefer the warmer side of their tolerance limit if they can get it. If they are inside birds and you keep them above 5 degrees (41F) they will never have a problem as long as they are seasoned birds and you don't take them from a non stop heated house and start leaving them in freezing areas abruptly.
Anything over 10 degrees (50f) for inside birds is a comfortable life and 20 degrees (68F) is pretty much a tropical resort.
If you live in a hotel, it's your only pet and you named it "Tinkerbell", spend the money on heating the house to 20C and plant a tree to combat global warming because it's nice to spoil pets.
If not, don't worry, your buddies won't hold it against you so long as they are not stuck perching on metal, to close to freezing or unable to escape cold moving air 😉