New Puppy owner with a couple ???'s....

Welcome to the forum!
 
While you will doubtless find plenty of help here...we do have an entire Behavior and Training area you might also check out. Searching the archives on "puppy mouthing" for example will yield a treasure trove of results []
 
If you'd like, I will happily move this post to the "Puppies" area of Behavior? there are very helpful knowledgeable folks there who don't always scope out every area each day...
 
Just let me know and welcome once again!

Here's the thing with kids and pups.  The pup doesn't see the kids as anything other than litter mates.  Sure they LOOK a bit different, but they are on the floor a lot, they run a lot, and they make strange, high pitched noises, especially when they get nipped.  So, the kids need to be trained as much as the pup does.  And that's the tough part.  The kids need to move slowly and steadily around the pup, to speak softly and not with the excited little kid voices most have 99% of the time, they shouldn't play on the floor for now and they should never be left unsupervised with the pup.  Not even for a second.  Stuff just happens too quickly.  Children under 10 are the most bitten humans and this is mostly where it starts....pup sees them as playmates, pup nips and the child reacts and as pup grows, he doesn't learn that nipping the KIDS isn't cool.
 
Supervise every second that the kids are with the pup and ALWAYS have something to shove in her mouth when she nips the kids.  I foster and usually get litters.  When I have a litter I am NEVER without a fanny pack stuffed with good chew stuff.  When someone chews on me, they get "uh uh, no bite" then given a toy and told "THIS is what you can bite" and then praise for chewing on IT instead of me.  So when the kids are around the pup, be sure you have plenty of chew things at your finger tips and correct and redirect.
 
When I walk pups in the cold and snow, I play it by ear.  If someone slows down I'll pick them up and continue walking....if he squirms and wants down, I let him down, if he snuggles in, he's had enough and I'll carry him for a bit to give him a rest and then let him try again.  Crazy dogs tho seem to love the snow and cold so just keep an eye on things and play it by ear.  I don't protect paws personally, but I've got german shepherds who are pretty sturdy.
 
Length of walks, again, play it by ear.  If the pup seems tired, stop.  Multiple short walks are better than one or two really long ones.  No sustained running, especially on hard surfaces until the pup is grown, but her running and stopping of her own accord is fine.
 
And, welcome to idog.

Your kids are also old enough to start training the dog too. My two year old can even say "Gacy no lick." While it doesn't always stop the dog from kissing her, it's good practice! The older one can help with actual training and commands, also will help the dog see them as "not a puppy".

Welcome!!  Be still my heart, a little E.S!  Honey is adorable!  I'm a Wisconsin ES owner, too. 
 
When my Dash was little, he was a terrible biter, too.  That's probably the worst problem we ever encountered.  At that age, we pretty much ignored him when he did this, which was a lot, and stopped all play.  It took a long time. 
 
My Dash ended up having surgery for lousy hips and I probably over-exercised him, too.  So I won't attempt to answer the exercise question!  I think that's a tough one, as it depends on predisposition to H.D., too. 
 
I really am looking forward to seeing pics of Honey!