Your location says "Kansas," so I'm going to call it a Holland Lop, OK?
I've been breeding Hollands for more than 20 years, so I can reflect on a lot of intentional litters.
If you'll excuse me, I am about to do a major exposition on the dwarfing gene, before I get around to your question (I hope you don't mind).
As you said, the Holland employs the dwarfing gene. For those who don't know, the dwarfing gene is what gives you the really compact animal described in the breed standard of many small rabbit breeds. An animal with the dwarfing gene has shorter ears, shorter legs, a shorter, rounder head, and a shorter body than one without the dwarfing gene, and weighs half a pound to a pound less. The problem with the dwarfing gene is that it is a lethal gene, which means that a baby that inherits it from both parents will die within days of birth.
Virtually every Holland Lop that makes show weight has one copy of the dwarfing gene, and one copy of the normal growth gene. It has a 50% chance of passing the dwarfing gene on to any given offspring, and a 50% chance of giving it the normal growth gene. Breed two such animals together, and you will have some that get the normal growth gene from one parent, and the dwarfing gene from the other - we sometimes refer to those as "true dwarfs." Some will get the normal growth gene from both parents. These are sometimes called "false dwarfs," though in the case of does, I have heard them referred to as "brood does" (I know someone who calls them "Big Ugly Does"). And of course, there are those who get a copy of the dwarfing gene from both parents; these are often called "peanuts." Peanuts are visibly smaller than their viable siblings at birth, with an oddly shaped head and an underdeveloped look to their hind ends. Their digestive systems are seriously deformed or even incomplete, so they generally starve to death within a couple of days of being born.
In some European countries (Germany, for one), it is illegal to do intentional breedings that will result in offspring that inherit genetic conditions that result in death or "suffering." This doesn't mean that you can't breed dwarf rabbits there, just that you can't do dwarf-to-dwarf breeding. This is where the "false dwarfs" come in. Because the false dwarf doesn't have the dwarfing gene, it can't pass it on, so no matter what rabbit you breed it to, it can't have peanuts. Every baby born to a false dwarf has a chance at surviving; if it dies, it won't be because of the dwarfing gene.
A lot of people keep false dwarf does, and breed them to a "true dwarf" buck. False dwarf does aren't really "ugly;" the trick is to learn what good type looks like without the dwarfing gene, and pick those does, the others get sold as pets.
In the Holland Lop, the average litter for a true dwarf doe is 3-5. A false dwarf doe usually has a slightly larger litter (4 to 8, IME). Some of the true dwarf doe's babies may be peanuts (if you are really unlucky, you can even have a whole litter that are born with the lethal combination), but a false dwarf can only have true dwarfs and false dwarfs - no peanuts.
Anyway, back to your question. A first-time mom is a first-time mom, and you can't be sure what she'll do. A lot of them do mess things up their first time around - not putting the babies in the nest box, not pulling fur, not feeding them - there are a lot of mistakes a doe can make. A doe that is a good mother often has daughters that are good mothers, but since that isn't something that gets you points on a show table, it tends not to be part of the selection process when someone is choosing breeders. But if you have a doe that does her job (and some get it all right from the get-go), and you have a reasonable sized litter (at least 3), there is an excellent chance that the kits will survive, particularly since you are protecting them from the extremes of temperature that kills so many litters at this time of year. When I expect litters during cool weather, I bring my does in (I call my hall closet "the maternity ward") just to offset the possibility of cold-related fatalities; even if the kits are born outside of the box, they usually survive so I can find them and correct the doe's mistake, if she makes it. Even if the doe doesn't pull fur, inside temperatures are usually warm enough to keep the kits alive. Now, babies can get trampled or lost due to other causes, so just having them born indoors doesn't guarantee survival, but it helps.