13 Week Husky Keeps Pooping in Crate

Our nightly routine is as follows.
We withhold food after 7pm. We take him potty before we go to bed, between 10-11pm (we always wait for him to poop and pee). My husband or I wake up between 2-3 am to take him out. We then take him out again at 6am and let him stay out after that.
We always clean the crate, toys and surrounding area thoroughly. We have taken him to the vet whom says that he is a perfectly healthy puppy. He hasn’t had any accidents in the house in over a month and doesn’t poop in his crate every night. Maybe once or twice a week but when we go to get him out of the crate he’ll be covered in it.
What am I doing wrong?

You seem to be doing everything right, but your expectations may be a little too high for such a young puppy. I would expect there to be mistakes at this age.
When you say that he is 'covered in it', does this mean that his poop is soft? If so, his diet might need to be changed to a food that will produce a firmer cigar shaped motion.
Also, does he have enough room in his crate to allow him to have a mistake without having to do it on his bedding?

He has good poops. Not watery or loose at all. What I mean by covered in it is, he’ll poop and then walk around in it. So his paws will have poop all over them. Sometimes it will be on his tail as well. He has enough room to stand, lay down and turn around. We removed the bedding after the first few accidents.

I think the point was, if he only has enough room to stand and turn around etc he won't be able to get away from where he's pooped so will inevitably be treading in it. He will of course need a larger crate as he grows if you intend to keep him crated. He's too young to be 100% reliable at this age and probably won't be until around 20 weeks. One of mine went in his crate last week and he's 9 but had a bit of a dodgy tummy and that was obvious by what he produced but if as you say your pup has firm poos then it's just a case of carrying on with his training until he is reliable.

Toss the crate in the garbage, problem solved. How would you like to live in a crate?

Lots of dogs like their crates, they see them as a den. It's up to the OP whether she uses one or not.

Actually no dog that likes it's crate has any choice, so rather than liking the crate they are merely too timid to do anything about this situation. Now no dog defecates where it sleeps, this is natural, thus this dog has no intention of sleeping in a crate and is rebelling. Good for the dog.

Have you ever slept in a crate?

Totally agree.
I would not remotely consider puting any dog I've had in a cage. If ours wants out he gently taps the door Same in a hotel or a holiday cottage. Shutting them in a cage, or crate if you prefer to call it that, is something for wild animals, not a domestic pet.

What tosh of course some dogs have a choice over whether to use the crate or not, you leave the crate in situ with the door open and invariably find the dog asleep in the crate even when they have other beds available to them. Or leave it in situ with the door closed and find the dog pawing at the crate to get in. Your dog may not like to use a crate but that doesn't mean no dog likes to.
The dog crapped in it's crate because he doesn't yet have control of his bowels, he wasn't showing his displeasure at being shut in the crate. No doubt if the crate was open he would have left his sleeping area to poop, but as he couldn't, he didn't. Yes it's unnatural to poop in it's bed so why do it to express displeasure, he did it cos he had no choice.

Right you wouldn't shut a dog in but you'd cage a wild animal, and that's not cruel because?