They won't hatch now after being exposed to such extremes of cold. Remove them and replace them with a few dummy eggs, so that she will continue to lay in the same nest, and you can enjoy the eggs while she is still around.
That leads to another issue. It seems as though she has free reign of the property. No matter where you live, if she has no protection from predators, she will eventually become their next meal, especially with winter coming. It's only a matter of time. I guarantee it.

Also, duck eggs are edible and are very good for baking. You can use them as you would hen eggs, but the whites tend to be rather thicker and almost translucent (I know, sounds weird and impossible, but try it) when fried or scrambled, so I can't bring myself to eat them. (Yes, I know looks and texture have nothing to do with taste, but my stomach doesn't believe it.....) But, I have been told by others that they make very moist cakes, breads, etc., anything that you add well-beaten eggs to. So you can collect them and use the eggs.

Since the old eggs are of unknown ages now, be VERY careful collecting them, and if you throw them out in the woods, do it FAR from the house - if they go into the garbage, pput them into a sealed bag or container - as old eggs can be rotten, and rotten eggs STINK!

Hello and thanks much for the replies. Patrick, they do have a shelter (a chicken coupe... or duck house now :) ) and we have a chicken wire fence around a very small yard around it but when they got old enough, we let them out (you're right... we started with four and the dog got two of them before we made her understand that these ducks are not for eating and she now protects them as members of the 'pack' ). We have food and water and a little kiddy wading pool inside the fence for them but they bolt out of there as soon as they see us coming to shut them in and the male has discovered a way (probably over the top) to get out of the fence. We shut them in the duck house a couple of nights but it took alot of chasing them around to get them to go in there. Any suggestions? I was hoping that maybe between the nest dug into the ground, her feathers and leaves, the protection from the wind, and her body heat they may survive ... but no? She is really protective of her nest. I even dug a little place in the bedding in thier building and put the first scattered eggs into them (which have now been blown out and used for pysanky) and shut them in the building for a couple nights (which is equipt with a heat lamp) but they seem uninterested in it. Maybe I should move her eggs (even if they are not 'viable') into the building along with her nesting materials??? and turn on the heat lamp... I almost hate to encourage her to lay more eggs in a nest that is not in the building.

You really need to get a copy of Storey's Guide to Raising Ducks by Dave Holderread. It's a great book, and will answer many of your questions and more. You're making a lot of common novice mistakes,and unfortunately have gotten some incorrect information somewhere along the way. Time and space doesn't allow for giving you all of the information that you need here. Best of luck with your ducks, and I hope that you are able to get a copy of the book while you still have them to enjoy.

I recommend keeping your ducks protected at all times..especially in the winter when predators are even hungrier and more desperate. An unprotected duck won't stand a chance.
I keep mine in a large fenced area with my hens ,the open part of the area that holds the pond is netted over the top to prevent any hawks or other nasty predators from harming them. Then at nightfall I always put everyone closed up in their coops. If I couldn't do this I wouldn't have them. I have a large amount of coyotees here,and wolves.
The ducks only took a couple of times of herding them in at night until they got into the routine...they see me coming and I say "c'mon to bed guys"..and off they march into their duckhouse for the night. It's really cute,and very safe,,let's me sleep at night :)
I highly recomend the protection.. :)

Thanks for the good advice, beeliz! I will try this. I wish my ducks would go where I want them to! We started them in the fence and I assumed they would go back in when I fed them. We had ducks one other time years ago and they followed me all over the place... thought I was thier mama :D . But these ducks... we've had them since they were babies and I always say (silly as it sounds), "duckduckduckduckduck" when I see them, walk by them, feed them, etc... but they still don't want to follow me. Well, I'll herd them into the fence (sometimes I can lure them with the water running in the baby pool but they wont get near it until I walk away because they know I'm going to shut them in and they hate it. I'm really fortunate to have my dog (she's one of a kind) because she does keep predators away. We praise her for 'checking on' the ducks and now she treats them as she would one of the kids (it's so cute). She's about a 65lb. dog and smart as any on this planet :) But I will try to get them to leave that nest (they're BOTH on it all the time!) and go into thier fence. I'll have to figure out some sort of net to go over the top but that still allows us to walk in to get to the duckhouse.

I know how you feel about them sitting on the eggs...you feel bad eh? try moving the whole shibang into their night house...maybe they'll stay with it...if not,at least you know you tried right? And you'd rather have your 2 ducks without their eggs than no ducks at all.
I ordered a poultry net on the internet...try looking under "poultry netting" or even fishing netting,and you'll get a good deal. I attatched mine to the chicken wire fence I have..it was quite easy,but it was spring and not -20!! Good luck...and your dog sounds awsome!

You can buy "deer fence" a very lightweight mesh that is fairly wide and pretty long, I put it over the duck stall before we put the roof on it. It works very nicely to keep the ducks inside.

I've found that you have to stop feeding the ducks in the morning so they are hungry enough to come in at night. Otherwise, if they have free choice feed, they ignore the dinner signal (shaking the grain bucket, and for my flock the call is "goose-goose, goose-goose" because I had geese before the ducks.)

I am going to experiment with putting duct tape on the mesh edges to make it easier to secure the mesh to the cages. We'll see.

If you really want to raise ducks, you can always get an incubator, collect the eggs, date them with a pencil, roll the eggs daily until they hatch. Then you will have LOTS of peepers!

Otherwise, the first hatch is the hardest for a new mom. AFter the first one, they get the idea much better.
good luck,
Kitty